Look out of the window. I haven't seen a cloud all afternoon, I was teaching the 5th lesson for a PPL. Weather is great! Has been for months, almost without interruption. If it's sunny fly, if not, talk about flying.
Yes weather is a consideration in the winter in the UK, it cannot be denied. You will often find, though, that the worst is over before January, I have logged a fair few VFR hours in a February when we often get a lot of clear skies, and that was up country (here we have more sunshine than anywhere else in the UK, so it is not an average comparrison). I did my CPL in the winter, and the school I was with running down for Christmas and a slight illness did more to delay me than weather.
Certainly the sim time for both CPL and IR (up to 43 hours of the 50-hour course, if that is how you want it!) is independent of weather, but as FFF says much of the IR can be completed in fairly poor weather. Even CPL flying is less weather-dependent than PPL.
When I went to the states many years ago for a PPL it turned out I would have achieved it more quickly in the UK, as the weather was poor over there. Couldn't have afforded it though.