In reply to Weshgro:
The colder months are much better for bouldering, although there's also a much higher chance of rain (or snow). Any time from now to May will be pretty good provided you're lucky with the weather. In the depths of winter, it really is very cold and you're generally limited to the south-facing sheltered venues; the good bouldering days with no wind, bone dry, bright blue skies are few and far between - but they are fantastic.
Personally, I would stick to the sandstone and gritstone. The Peak is excellent, but the bouldering in Yorkshire (an hour or so north of the Peak) is also on gritstone and is actually better than the Peak.
Places that I consider essential in the Peak and Yorkshire are:
Slipstones - world class, best rock in the world, beautiful setting
Caley - great venue with excellent climbing but often damp and a bit of a dump (by a busy road, litter and dog turds)
Stanage - classic. Go beyond the popular Plantation area (much of which is not that amazing) to find the best bits.
Bridestones - slightly crap sandy rock, but some amazing problems. Atmospheric.
Cratcliffe and Robin Hood's Stride - a beautiful place, lots of nice safe problems
The Roaches - spread out over a big area, with many perfect problems in a beautiful setting
Another great place but rather out of the way is St. Bees on the Lakeland coast:
http://www.ukclimbing.com/videos/play.php?i=1807
Lovely sandstone.
I haven't been to Northumberland, but there's plenty of sandstone there too.
Personally, I would avoid limestone bouldering like the plague. It's appalling. Not as bad by any means, but still horrible IMO is bouldering on the volcanic rock of the Lakes and Snowdonia. Others will disagree, I just think climbing really hard moves on sharp, polished rock is deeply unpleasant. It also rains continually in the mountains over the winter.
That's a start for you. There's a book called Boulder Britain that might be just what you need.