You will need quite a sophisticated boat if you are going to be happy spending UK winters on board.
Must haves - Hot water, high capacity dry heater, really good electrics and lighting designed to cope with demands of long winter nights. Lots of good warm cloathing so you will be comfortable outdoors in all waethers. Somewhere to put coats and wellies without them dripping below - ether enclosed wheelhouse or full cockpit tent. Legs/twin keel ability to dry alongside or up a creek is a must.
Even the best equiped boat is not going to do much in Nov/Dec, its not so much the temp as the darkness so you need to find somewhere snug and secure to hole up. Creeks/mud berths etc are exellent for wintering but sometimes take a bit of finding. Alternative is to get well up one of the biger rivers oronto a section of canal. Might be worth considering hopping accross to S.Brittany for 3 moths if you can. From Feb onwards there is some glorious sailing. I did try it but found that because I work full time it wasnt practicable to spend winter onboard unless in a marina but the boat was quite basic then. Even with the boat finished I think I would find it tough if I had to go to work, rowing ashore every morning in the dark when its freezing and blowing takes perseverence. If I didnt have to work reckon it would be practical because you have a much wider choice of spots.

As far as budget goes I tend to go with the Pardys formula of about 60% of what you spend on the bank. The previso in the uk is that marina fees have become so high that getting stuck for even a few weeks in the wrong place could blow the budget for a year. Unless you are ruthless about not using them marina fees will probably be you biggest singe expense, even just dropping in once per week for fuel & water + shower & laundry could set you bacl Ł1500-Ł3000pa depending on area. Food and boat maintainace are probably the other main areas at about the same level.

On boat size I think you tend to want a little more space for higher lats because you spend more time below and need more cloaths. Length O/A is a poor guide and the only reason so much attention is paid to it is because it controls berthing charges, boat prices tend to go on wt not length amd lenth W/L x Beam is a more reliable assessment of space. I would want a min of about 6T, 26ft waterline, 10ft beam. Bilge keels are fine but should have metal shoes fitted to the bottem and you need to check that the design was intended to regulary take the ground because a lot arn't. Cat is also a posibility and dont rule out long keel + legs. Quite easy to ues once you get the hang of it and the strongets design + very good leaning on a wall.

I have been based at milfor haven for the last few years and before that was in Morcombe bay. I lived abourd in UK for about 3 years but the last 2 have been back on the bank due to work/family & refitting. Intend setting off again next year heading for N spain this time. PM me if you have specific questions