What was the reason for inflation in Britain after the Black Death?

This is a very simplified example but hopefully it will help:

Assume that there are 10 nobles and 100 workers. Each noble has 10 fields and uses at least 1 worker per field.

Nobles have financial commitments and a standard of living which they wish to maintain. They pay the workers 1 pound a week to work on the fields and each field is equally profitable.

Workers cannot easily move around as nobles elsewhere are paying roughly the same and already have manpower so the wage is fairly static. The good and sundries that workers can by is within their price range as there is no point charging more as they will not be able to buy it.

Lets assume that your calculation about the ratio of deaths is equal and each class loses 50% of its members.

There are now 5 nobles, 50 workers (25 of which have no nobleman to work for)- each noble still has 10 fields which requires at least 1 worker per field.

Now each noble now only has 5 workers and therefore has 5 empty fields and will therefore make less money but they still have their commitments and standard of living which they wish to maintain.

PANIC!!!!

There are various workers which no longer have anywhere to work but still need to feed their families.

Nobleman #1 is called Alfred has the idea that he can pay these people to come and work for him. Nobleman #2 is called Bill and has the same idea.

Alfred offers them 1 pound to work on his field, Bill offers them 2 pounds. The rest of Alfred's and Bill's workers realise that they have power - they are a scarce resource so they contact noblemen 3,4,5 (Charles, Dave and Edward) and ask how much they would offer. Edward realises the value of having more than 1 worker per field now that they can buy them on the free market and begin buying up the finite labour source as an investment as he had the backing capital to do it, unlike poor Alfred.

Eventually Alfred manages to persuade 6 workers to work for him at the extortionate price of 6 pounds per week. Hence he was paying 10 pounds a week for 10 fields worth, he is now paying 36 pounds a week for 6 fields worth. This is awful and he cannot afford to buy that new set of armour. He tells everyone who will listen how greedy and lazy the workers are.

The workers who work for Alfred now have 6 times the buying power they had before so they go to the market/tavern/whatever and buy everything in site. The next week the owners of the market have felt the effect of the increase in cost of workers and have to charge more for the goods to make a profit hence everything becomes more expensive. If the market owners think they can get away with it they also tag some extra on the increase to make some extra money.

Suddenly Alfred's workers are not that rich in real terms and demand a pay rise or they will leave and work for Edward who is desperately offering massive amounts of money to anyone who will work for him.

However, everytime they get a pay rise to buy more things the cost of making things goes up (as their wages are part of the cost) and an inflation spiral begins.

Due to the massive increase in prices at the market and the cost of labour the noblemen find that they are not able to make as much profit as before and struggle to afford to pay the worker enough to keep them let alone maintain their standard of living. Hence they are far worse off.

Workers are better off but the inflated costs of good is crippling some people who cannot get the high wages for whatever reason.

Caveat

You said, "it could only improve the life quality of everyone since more land was available per person." - that would only be true if the two classes benefitted equally from the land. That is an assumption that will lead you very far astray. @Stefan has provided an extended example. Essentially however, if the benefit of land was skewed 90% nobility 10% commoner, then the quality of life of the nobility is reduced FAR more than the quality of life of the commoner. (this is apart from the fact that it is very difficult to reduce quality of life below subsistence; at a certain point, quality of life is "sticky downwards".)

Serious Answer

You assert,

If the number of labourers and landowners was reduced by the same factor, it could only improve the life quality of everyone since more land was available per person.

I don't think this is a supportable assertion. Let us assume that prior to the black death land was fully utilized (that is to say the cost of bringing another unit of land under cultivation/production would cost more than it was worth.) After the black death, 1/3 of the population is dead. The simplistic assumption is that the population will continue to cultivate 2/3 of the land and everything will continue as before.

Reality is a bit more complex.

• Loss of specialization. I don't have citations, but I'll assume that most non-farming skills were represented by the minimum number of people. Skilled labor requires a production surplus, and the point of a feudal economy is to direct production surplus to the noble class; laboring classes are to be held at the minimum subsistence level. Every skilled laborer (baker, miller, blacksmith, etc.) lost to the plague cannot be replaced. Skilled professionals can be induced to move (Town A hires a journeyman blacksmith from town B). Effectively speaking, the only way to move skilled labor is to raise compensation (wages & non-wage benefits). Surges in labor wages will create inflation unless the central bank eases monetary policy. (For simplicity, let's assume that the central bank is ineffective. They're crippled by a specie based economy and lack the underlying theory )
• Sticky standard of living. When standards of living rise, people are happy; when standards of living fall, people act to preserve their standard of living. Historically this trend is more effective than it appears on the surface. People are much more likely to act to prevent loss than they are to facilitate gain. This is where the flaw in your assumption is really important; Nobles have the political and economic power to preserve their standard of living despite the drop in cultivated land. This is reinforced by their discovery of the limits of their political power. If they ate meat 3/week prior to the plague, they expect to continue to eat meat 3/week after the plague, despite the loss of 1/3 of the cropland. The only way to maintain that standard of living in the face of a decreased labor supply is to acquire labor. In the short term, estates are consolidated from those who have died to those who have survived; in the medium term, the only way to preserve the standard of living is to acquire more labor, through conquest, or through promising greater benefits. (I'm uncomfortable discussing the "wages" of peasants, but that requires discussion of serfdom, chattel and other concepts that are more complex than we want to deal with here).
• Unequal consequences. The plague killed 90% in some regions and < 10% in others. That means that in some towns there was actually a surplus of labor, and in other towns there was a severe scarcity. Both surplus and existential scarcity will always affect prices. Surplus labor will move to where it can be more productive. It was technically illegal for a peasant to move to another estate, but practically speaking, the peasants would move to where they perceived their best advantage. That had the effect of forcing a rise in the price of unskilled labor (And a secondary effect of weakening the political restrictions on unskilled labor, which threatened the standard of living of the noble classes, which reinforced all the other effects mentioned.) In regions where the labor supply fell below the minimum necessary to surive, there were three alternatives. (1) dissolve, and move to a new location (as above, this increases the effective cost of labor), (2) Acquire new labor (which directly raises the cost of labor), or (3) vanish from the economy, which had severe social consequences; for example, if you drop out of society, you lose the social civil contract - you have no recompense against brigands, you lose the benefit of religious services, and your chance of begetting children drop radically.
• Diversity of skill. In both skilled and unskilled labor, some individuals are more productive than others. In times of labor scarcity, this drives their wages up significantly. Even if the local labor pool is simple and stable (what you describe), very good farmers have at least the option of illegally moving to an estate where they have the chance to become yeomen. Some nobles attempted to enforce the law, and discovered that this made their most productive farmers more likely to flee to somewhere they would be rewarded. (in a conflict between economics and regulation, long term, bet on economics).
• Land quality differs - those who remain alive will selectively cultivate the most productive land, allowing the least productive land to go fallow. Productivity will appear to rise somewhat, although probably not very significantly. I mention this for completeness.
• Capital deepening. Those who remain will also have roughly 1/3 more tools. For example, the plow which was shared amoung 10 villagers previously is now shared among 7 villagers. This results in a rise in productivity, and a rise in wealth.

Summary: Scarcity creates an upward pressure on labor compensation. In the absence of a skillfully managed monetary policy, that upward pressure will cause a rise in overall prices (inflation).

The question of the economic consequences of the black death is perhaps one of the most fascinating I can imagine. Just as, if not more fascinating, is the interplay of politics and economics, and what we learn about being a human animal.

The classical answer

This is a classic wage price spiral arising from a supply shock. The death of 1/3 of the laboring class resulted in in a reduction of the supply for labor, and a resulting rise in the demand for labor. According to classical economics the rise in the demand for labor should have caused labor to flow to the affected area.

Of course this is also an illustration of where classical economics doesn't apply. Prices (including the price of labor) in the period were set by custom and law. It was illegal for labor to move from one employer to another. Ken Follett described this rather well in Pillars of the Earth (or possibly World Without End; the books blur in my memory). This is an excellent example of public choice economics; those with political power use it to protect their privilege against threats which emerge from economic constraints. See also Rent Seeking

Many current studies of rent-seeking focus on efforts to capture various monopoly privileges stemming from government regulation of a market. The term itself derives, however, from the far older practice of appropriating a portion of production by gaining ownership or control of land.

What passes for a humorous answer

Of course the plague struck throughout the labor market, raising the price of labor everywhere. There were very few places where Britain could have imported labor. Production of labor remains constrained by the very inefficient labor production mechanism - it takes 10-15 years to produce a new unit of labour (and in the time period, approximately 50% of the new production of labour failed to pass quality testing). Modern labor production is more reliable, but legal restrictions impose a minimum 16 year cycle on the production of new labor. Although production of new labor has been effectively restricted to less than 50% of the population, analysis of the data fails to demonstrate a significant increase in the welfare of those who have a monopoly on the production of new labor.

This is also a case where it is difficult to justify Friedman's Maxim "Inflation is always and everywhere a monetary phenomenon.", and is therefore an interesting test case. The knee-jerk response to inflation is to contract the money supply. This is very difficult to do in a specie economy.

Final notes

1. This is fundamentally a question about labor and the history of labor; I hope that @SamuelRussell will weigh in. This is one of the periods of history where his analysis is probably going to be more accurate than mine.
2. Someone asked why the relative situation matters - I have no clue how to prove this, but the only useful assumption in economics is that humans will always pay attention to relative wealth. There are entire cultures built on this notion (e.g. the Navajo, who condemn any person who is more wealthy than his neighbors). This is a way deeper topic that I'm not qualified to answer, but the only safe assumption is that a significant fraction of the population is willing to act to preserve/acquire relative wealth differences.

Inflation has been defined as "too much money chasing too few goods," or in this case, "too few people."

The supply of money, M, was fixed by the number of coins in circulation, which in turn was limited by the amount of available precious metals. When one third of the population, P, died off suddenly, the former relation of M to P became M/(2/3 P), meaning there was 50% more money in circulation per person. If people had formerly been fully employed in producing goods, G, that would also change the relationship of M/G to M/(2/3 G), again, 50% more M per good. That's why goods and wages would rise about 50% in monetary terms. They probably rose less in "real" terms (after the resulting inflation).

The nobles complained because they had most of the money (and most of the land). With a sudden shortage of labor, the nobles' land and money didn't go as far, causing "inflation." The laborers prospered, but few of them could read or write, so we don't hear their side of the story.