My personal solution are down jackets/coats. Fleece and the rest of Barbour type of traditional English attire is not warm enough. Depends how much you are prepared to spend. Canada Goose jackets are very warm and quite trendy
There are plenty of decent branded waterproof padded jackets for under £150 which should do the trick - Karrimor, Berghaus, Rab, North Face etc. Go for something breathable - Gore Tex is generally pricey however you can pick up an outer only for less than £100. You could then buy a cheap base layer and fleece of which there are plenty.
I picked up a very good breathable Sprayway jacket from our local department store in their sale for £30. If you're looking for a bargain the best time to buy is of course at the end of the season i.e. the Spring.
Echo previous posters comments about layering, hats and gloves. Don't forget about your feet - when out and about for an extended period of time I usually wear a pair of lightweight summer walking boots with a couple of pair of socks, a decent inner pair with a thick walking sock. You could also try a pair of trail/approach shoes.
Forgot to mention - check out the Go Outdoors chain of shops. Not sure where our local one is (I've been to the ones in Oxford and Swindon - the latter is a shortish walk from the train station if ever you have cause to stop there). They've a good range of some of the better brands, however I'd personally avoid their own-brand North Face rip-off (I think it was called something like North Ridge).
For outdoor doings, I live in one like this from the beginning of November and for the next 5 months at least. Costs just under 100 quid, is hard wearing, water and wind repellent and roomy enough to wear many layers under it when it gets really cold. Despite copping a lot of ridicule and ribbing from family and friends for looking like a road worker/farmer/kindergarten teacher, I love this very comfy and functional garment.
Counter-productive to talk to climbers and the like - they are looking for things like taped-seams which are necessary bivouacking on a ledge, but not for staying on the streets.
Very few if any places in UK where you would need to Bivvy when climbing but climbers / walkers often have long walks into get to the start and they like to be comfortable.
The only small weak point in the above is the tips of the gloves as I have not yet found a glove where the insulation is wrapped around the finger-tip: manufacturing methods dictate that the fingers are in two or four pieces which come together at the tip which has to be devoid of insulant. That really is however the last percent.
I found using a very thin Glove as inner layer, slightly heavier over them then followed by mittens keeps the fingers nice and toasty
Kanuk makes something for every budget, and they'll ship anywhere. I've had a Saguenay for the past 12 years, a bit pricey, but it's what I call a good urban parka (anorak I think it's called in the UK). With a sweater or a fleece underneath, it's good down to -30.
If money's no object, this is what they wear in the Arctic and Antarctic when they go outside.
I bought a jacket from Cabelas a couple of years ago, extremely warm but very heavy. If wet I think it might pull the coathooks off the wall. My original post was aimed at staying warm indoors. The sock shop is advertising hotsocks or something. I agree with earlier posters, if the extremities are warm that's half the problem solved. Have you considered a willy-warmer?