Summer weather is something rather unpredictable in Western Europe. It CAN rain all the time. There is no guarantee that the June weather is better than the May weather. I have been in England some years ago in May for two weeks and had it all: so much sun I had to buy a sundress and streaming rain.

In the last years however UK weather has sometimes been better than it's reputation. May has the advantage that there is no green than UK green

I think the Chelsea Flower Show is yearly. 2005 it will be next week:

Chelsea Flower Show