England in January

It depends!
What do you call too rainy? As someone once said, there is no such thing as bad weather, only inappropriate clothing.
January can be wet, but like anywhere, it is becoming increasingly difficult to predict weather.
The thing about London is that there are so many attractions which are indoors, and the transport system is both good and dry.
I'd go for it.

It’s not really the rain or the cold that is the problem but the lack of daylight. It gets dark at 4pm. This is maybe ok if you’re in London but not if you want to explore the countryside.

London gets about the same amount of rain on a monthly basis all year round. But it does tend to feel wetter in the winter because, as noted, it’s colder and darker.

England is a big place - bigger than it looks, and with very diverse weather. The weather varies considerably around the country. Where are you talking about? Cornwall? Carlisle? Newcastle? Norwich?

Or by England do you mean London and the Home Counties?

Thank you so much for all the responses this far. My plan was to use London as a Base City, explore as much of London as I can see and then do like day trips to the Cotswolds, bath, and maybe do four or five days in Liverpool as despite being before my time I am a huge Beatles fan

All those places will be fine to visit in the winter except the Cotswolds (which are a bit overrated anyway compared to other scenic areas of the UK.). Rick’s general advice for Europe that in winter big cities are better than rural areas and small towns holds as true for the UK as anywhere else. I like Liverpool a lot (and I was there in winter). Five days is much more than enough for the Beatles sites but not too long if you do some day trips such as Chester and Manchester. What I did was split five days between Liverpool and Manchester and that worked very well. I did other things than Beatles sites when in Liverpool. There are some good museums there although one of the best, the maritime museum, is currently closed for renovation.

welcome to the Forums, darrenr1

I grew up in the Cotswolds so I know of what I speak.

The Cotswolds in January is drab, cold, wet, shut up, Dry January (not the weather, but for not drinking in January after the excesses of the Christmas / New Year season), and very dark.

The villages won't show to their best - the beautiful Cotswold Stone houses will be drab because of no or very little light. There will be glare when there is any light because the roads never dry, and the stone holds on to the moisture, the sun if it should appear at all will be very low from the south also contributing to the glare. Any thatched roofs will also be drab in that light.

Expect cars to have their headlights on all day - more glare - and the sun will be setting (what sun??) at or before 4pm, it will be under the cloud even if not raining quite dark by 3pm. Street lights will likely come on around 2pm.

As the Cotswolds are higher than the surrounding areas moisture often falls as snow or sleet.

What do you hope to see in the Cotswolds? What's attracting you?

And, very importantly, how will you get around? Car? Taxi? Big bus from London? Walking?

or it might be bright brilliant sunshine for the whole time. (pigs might fly)

Our rain is spread throughout the year. I wouldn't say that you have a greater chance of wet weather in January than you would do in July. Our weather is very difficult to predict. This week it's been 35C and sunny, the same week next year could be. 15C and raining.
London and the whole UK is geared up for when the weather is bad. There is lots to do indoors. You might even grt a cold, crisp spell. Hours of daylight are short in January, sunset at 4pm at the start, 5pm by the end.
Avoid the countryside and the Cotswolds. The scenery will be drab. Bare trees and muddy. Stick to the cities.
Outside London, Liverpool (Beatles), Chester, Newcastle, York even Manchester are worth googling. All easily reached by train.

WHY January. frankly, I don't like cold and wet myself.

The OP stated his reason for travelling in January. There's no reason not to. But sticking to the urban areas is a wise decision, given their many options for indoor activities. There are all kinds of choices besides just London and Liverpool.

A number of great country houses and other tourist attractions, mainly those outside the big towns, are closed during January for maintenance etc. It’s worth checking that the places the OP wants to go to are open. This doesn’t apply to major museums etc.

As someone who also lives in a rainy climate with short winter days (though not as short as those in the UK), I recommend also getting to the seaside when possible. More sky = more light. The seaside is easily reached from Liverpool and other cities, including Newcastle, which another commenter mentioned. See also: Edinburgh, which is not in England, of course, but it's on the same island, so...
Also, most of the time, the rain is falling so slowly that it really doesn't stop you doing anything. Shoes with a good, grippy sole, a waterproof rain jacket that fits over your various layers. A good tip I saw on the forum is to wear a ball cap (preferably waterproof and insulated if you can find one) to prop up the hood of your rain jacket.

We love a good rain walk but we also don't mind too much if we have to spend an afternoon in a pub with a fireplace, sipping, eating, reading our books.

It can be hard to find good places to travel in January in the northern hemisphere unless you're looking for winter sports-type activities. If you don't mind the very short hours of daylight that others have mentioned, there certainly is plenty to do here indoors, and if it's not raining you can even get some nature in- we once did a very nice walk along the Ridgeway on a frosty January day. That said I wouldn't base my trip around a lot of outdoor activities as the weather is rather unpredictable. Really the best things you can do in January are museums and pubs. As has been mentioned, certain types of attractions- such as historic homes- do close in the winter so have a look online for what you might want to see to check it will be open. Good luck with your planning.