Is it cold enough in England/London to have to wear a woolen/winter hat?

As someone who lives in a place where temperatures often reach more than 45C in the summer I can tell you a bit more about how someone from a moderate to warm climate deals with the cold.

Recently I was in Amsterdam which had rain/sleet/wind - so, almost London, except no red busses :). It was windy - but it did not snow (snow is not expected in London for at least the upcoming week, as per BBC weather).

I am by my own admission not averse to cold weather; I enjoy it but even I can tell you that a warm hat goes a long way into reducing the perception of cold.

You can just wear a hat, and a windbreaker / rain jacket and you will be very warm.

If you are a husky person (I am 5'8" and 120 lbs) you will find that walking around easily increases your body temp so the first thing you will feel is instant warmth - it is often easy to overdress for the cold and then walk around with a coat on your arm because its just too damn hot when you put it on.

So, I would recommend:

1. Dress in layers rather than one or two very warm pieces.
2. Carry a warm seamed cap (often called a beanie); one that you can pull over your ears if need be.
3. A scarf is good as well - keeps your neck warm and can act as a wind deterrent.
4. (Personal preference): Avoid a heavy jacket - because this will either make you extremely warm, or leave you extremely cold. These are good for when you are away from the metropolitan area where the effects of the weather (read: wind) are more prominent.
5. Some people prefer to dress in thermals (warm under garments) and then wear their "normal" clothes. I personally find thermals restrictive so avoid them.

Keep an eye on the wind forecast. Wind can increase the wind chill factor which will make it feel colder than it actually is outside.

I think the chance of you wanting a warm hat of some kind in London during this period is about 50%. The air temperature could easily vary between -5 and +10 celcius. If you don't have much hair on your head, or are planning to stand outside for periods of time, that increases the changes of wanting a hat. The typical temperatures in the UK earlier this week were close to zero.

Even if you're not planning to stand around outside, if you travel by train, there's a risk of having to stand on a windswept platform with little shelter while you wait for a delayed/cancelled train to appear.

I'm nearly bald, and frequently carry a cheap synthetic "woolly" hat in my pocket during the English winter. You should be able to buy one for about £5 if you shop around. You might want to consider thin cheap gloves of some kind as well.

I would say in the UK winter rain protection is more important than insulation. If you are dry the temperature isn't too bad but being wet leads to being cold and miserable.

So overall I would put a waterproof with hood above an insulated hat on the list of important stuff.

I live in the UK, I own a woolly hat. Some winter days I wear it and some I don't. Sometimes when I don't wear it, I wish I had. Coming from a warmer country you're likely (not guaranteed) to feel UK levels of cold more than I do, so you'll probably be more comfortable with a hat.

As a native, I would say that in the UK the weather is almost never cold enough that you need a hat in order to, for example, walk from a central London hotel to the nearest Tube station. A few minutes might be uncomfortable, but will never be harmful.

But if you're planning to be out in cold weather for an extended period of time, especially at night, especially if it's windy, especially if you're standing around doing nothing, then your ears may well start hurting and in this sense you "need" a hat. A scarf is also recommended, so that you can cover your mouth and nose if you're feeling it there.

In any case London is usually warmer than the average for the country since it's in the south and it's a large urban area. Furthermore, the weather forecast for London for the 6th-11th isn't "cold" as UK winters go: above 10°C except for the nightly lows, and never near freezing. So, perhaps colder than you ever get in the tropics, but you're only going to be miserable if you get it wrong, not frostbitten.

If your trip is pretty much entirely indoors with travel around London then you probably won't need it, except that some proportion of tropical visitors (I don't know how many) badly feel the cold. I have an aunt from Hong Kong who's near-constantly uncomfortable in the UK even in summer.

So, I would suggest taking a short walk aound the area once you arrive. If you feel the cold, do buy a hat locally, because the shops might not be open at the point where you seriously wish you had one: late at night with a long walk or wait ahead of you, or on a trip to some scenic location in the middle of nowhere. If you're concerned about cost then ask a friendly local for a cheap clothes shop. If you look around you should be able to find an unbranded beanie for under five pounds (it might be synthetic or blended rather than pure wool, but for the weather next week this doesn't matter). If you're not concerned about cost then go to the first sports shop you see in any high street or mall, and pick up a Nike/North Face/whatever branded hat for £15-20. Avoid team-branded kit from UK teams you don't support.