dont rely on the weather any time of the year in UK. Remember there is more to England than London. If you stay in Surrey there are hundreds of interesting places to visit without spending too much time travelling eg,Windsor Castle Hampton Court, the very pretty of chawton where Jane Austen lived . Also within reach is stonehenge Arundel Castle,Portsmouth where the Tudor Warship Mary Rose is displayed, Paris is only three hours away via the channel tunnel on the Eurostar train from Waterloo station London. I live in Surrey, let me know what kind of things interest you and Ican suggest an itinerary for you. If you like history, you will love it here.
,Florab

I usually try for mid-June.

Just before the crush of crowds and highest prices.

I prefer too warm than too cool. Not everybody does.

Also, the days are longer giving you much more daylight time to wander around.

Planning is the fun.

I would try for spring 2004.

You can do it by then.