When did furniture become common in the homes of most people in the British Isles?

SHORT ANSWER

The available sources suggest that even Iron Age roundhouses had some basic furniture such as benches and that, among the poor at least, the quantity (and probably the quality) of furniture did not change much for many centuries, perhaps until as late as the 16th century.

DETAILED ANSWER

Although our knowledge of furniture in the homes of ordinary people before the 17th century is somewhat sketchy, there are enough small pieces of information to get a general idea.

In Roman times, furniture was common in the houses of the wealthier members of society but we have little idea of the furniture inside the Iron Age roundhouses of the local population - it simply hasn't survived. However, recreations such as the one pictures below often show basic furniture.

Source: https://www.coam.org.uk/about-us/historic-buildings/iron-age-house/

Although the physical evidence of furniture may have long gone, it is not unreasonable to assume that Iron Age Britons who were able to build roundhouses would also have been quite capable of making basic furniture. In fact, an ongoing excavation in Cambridgeshire (Must Farm) of a site estimated to be around 3,000 years old has discovered remarkably well-preserved roundhouses with numerous items, including benches.

For the wealthy at least, after the Romans left, the amount and / or quality of furniture seems to have gone into decline:

The early Middle Ages were much poorer in household furnishings of every kind than the Roman world, but in the 14th and 15th century a growing affluence brought a major revival of furniture making, with many new types of cupboards, boxes with compartments, and various sorts of desks appearing.

However, the rich still had at least some basic furniture. In Saxon times,

Thanes and their followers slept on beds but the poorest people slept on the floor.

Several hundred years later, the amount of furniture of at least a reasonable quality was still quite limited even among the rich, judging by this passage relating to the time of Henry III (1216 - 1272):

Aristocratic households traveled frequently, visiting their various estates, conducting political business, and engaging in warfare. Most of the furniture traveled with the household—even the bedstead, a fairly large item, was bundled onto a cart or pack animal. This itinerant lifestyle dictated that furniture had to be kept to a minimum, and easily transportable. The total quantity of furniture and possessions in the home of an ordinary knight was probably comparable to that of a lower-middle-class wage earner today

Source: J.L. Singman, Daily Life in Medieval Europe

Recreation of the bedroom of Edward I (1272 - 1307) Source: https://media-cdn.tripadvisor.com/media/photo-s/0c/0e/3d/6b/king-edward-i-s-bedroom.jpg

Referring to a medieval peasant's hut, local histories.org states

Any furniture was very basic. Chairs were very expensive and no peasant could afford one. Instead they sat on benches or stools. They would have a simple wooden table and chests for storing clothes and other valuables.

Christopher Dyer, in Furnishings of medieval English peasant houses (pdf) notes that,

Though wooden peasant furniture has not survived, metal fittings such as locks and keys and hinges, and applied decoration from chests, are found on village excavations.

The interior of a rich peasant's hut. Poor peasants would not have had proper beds and certainly not a chimney. Instead, they would have slept on sacks stuffed with straw and had a hearth in the middle of the room, with the smoke drifting up through the roof.

This article on the History of Furniture manufacturing says that, in the Middle Ages,

Furniture was extremely basic, even in wealthy homes, chairs were uncommon; mainly, people sat on stools and benches.

For bedding, Dyer says

William Atkynson of Helperby near York who was not especially rich owned a featherbed. His less fortunate contemporaries slept on mattresses stuffed with straw or hair.. The really superior households, those of farmers with more than 100 acres of land, could aspire to fit a bed with a dorser, curtain and canopy, like Thomas Vicars of Strensall (1450) who had a green bed with a tapet (carpet) and a blue bed with curtains.

Much of the evidence for furniture comes from surviving inventories of peasants' homes. One of these, that of Richard Sclatter of Worcestershire lists bed, chair, tressle table, benches and chests in 1472 (note 'chair' is singular). There seems to have been only a small change over the next hundred years or so:

In the 16th century, furniture was more plentiful, but still basic; massive oak furniture was common among the rich. Chairs, still very expensive, were becoming more widespread....Seventeenth century furniture can be described as plain, heavy and made of oak; furniture among the affluent gradually became more comfy and decorated, made of walnut, then mahogany.

"This reconstruction drawing by Pat Hughes shows the house of Robert Dene (who died in 1552)...based on the inventory of his possessions attached to his will. This names four rooms...trestle table, benches, chairs, cupboards,...chests, beds..."

There was no mass-produced furniture before the 19th century. Any furniture of at least some quality would have been made by local carpenters. However, by the middle of the 17th century it would appear that furniture was common in most homes. By the 18th century, there seems to have been almost too much furniture:

Eighteenthcentury cottagers had too much free-standing furniture – including tables, chairs, cupboards and bedsteads, as well as spinning-wheels and laundry tubs – to have an open hearth in the middle of the floor.

Source: P. Sharpe & J. McEwan – Accommodating Poverty

Furniture has of course been in use for thousands of years before the advent of Christianity.

The earliest excavation of furniture artifacts in Britain were found in Skara Brae, Scotland. It is estimated to be from 3100-2500 BC. Due to lack of wood, the inhabitants are thought to have compensated by use of stone as the artifacts included:

1. Stone beds
2. Stone dressers
3. Stone shelves
4. Stone seats (That would fit as stools or benches)

Pictured below is evidence of furniture in the site:

Then we have Roman influence on Britain as well from the days of Roman Britannia. Romans primarily based their furniture on Greek designs. Quoting from Wikipedia:

Roman furniture was constructed principally using wood, metal and stone, with marble and limestone used for outside furniture. Very little wooden furniture survives intact, but there is evidence that a variety of woods were used, including maple, citron, beech, oak, and holly. Some imported wood such as satinwood was used for decoration. The most commonly used metal was bronze, of which numerous examples have survived, for example headrests for couches and metal stools.

In any case, it is safe to assume that Britons had furniture in 3100 BC. If I were to make an assumption, I would say humans must have made "furniture" as soon as they started wearing clothes/skins and found out that sitting on ground was not really good for their clothes.