Climate
London's weather is unpredictable, like much of Britain.
As London is towards the East Coast, rainfall's a lot lower than on the West Coast; even so, it does tend to be showery for most of the year, and even in the summer (June-September, or so) it'll probably rain on about 1/3 of the days in the month.
London seems a fair bit warmer than a lot of the rest of Eastern England. How much of this is to do with the density of heated buildings, how much to do with reduced wind at street level due to the (relatively tall) buildings around you and how much is just the fact that it's pretty far south I'm not sure.
Note that the tube doesn't have air conditioning. It would only probably need it for at most 20 days a year, and it was built well before such luxuries were considered. If you're in London in the height of summer, be prepared for other people around you to be a bit sweaty. (Similarly, many buildings don't have air con, although offices are much more likely to be so equipped than homes.)