Well, my knowledge of UK is limited to London.
My first trip was in month of May. The climate was pleasant - 15 degrees or so. It used to drizzle on and off. It would in most probability be a light drizzle and One would not get soaked. The Weather forecasts were quite correct.
There are many places to visit. Travelling around is a breeze. There are ample number of buses. The underground rail system is marvellous to say the least. All means of public transport are well connected.
If you are on a higher budget, you can go around in the taxis. From the outside, they look straight out of the 60s. But from inside, they are upto european standards. The best thin bout them is that they are really spacious. Can take in a lot of the Indian luggage as well.
A must visit place is the Millenium Dome. Then, there is the London Eye, the biggest observation wheel in the world. THe crown jewels are a must visit as well.
There are a lot of the usual travellors destinations, like the buckingam palace, big ben. One can easily find information on all such places in London. One can then decide, depending on the time available and personal preferences.
Comin to shopping, well its paradise out there. The Oxford street has everything from cheap bargains to the costliest stuff in the world!
From what I have noticed, the climate in London is good through out the year, and one can visit it in any season.