Personally I prefer the C152 - the C172 is much heavier on the controls, and being a shortarse I can't see over the instrument panel properly.
Any of the common fixed-gear singles: C150, C172, PA28, AA5, PA38, Pup... should take 60-90 minutes to get checked out, and there's absolutely no reason not to do so and then expand your flying horizons.
Just do your homework - manuals, checklists, airport rules, local area before flying anything for a checkout, and you should sail through.
Sywell and Duxford are worthwhile midlands destinations with stuff to do, also have a look at Halfpenny Green, which is always very friendly.
Britain has less good flying days in winter than summer, but when you get those good flying days, they can be spectactularly good. There is some sense in avoiding grass runways unless there's been a longish dry spell.
G