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.