I went to England, Wales, Ireland and Scotland in May. It was colder in Scotland and lightly snowing in the Highlands. I also went to London in August, and it rained the whole 10 days I was there.
According to my wife who grew up in England, September might be the best time of the year to vacation there. We went four years ago in September. We spend four days in London, and the temps were in the eighties each day with no rain. I can’t guarantee that it’ll be like that all the time. We’re going again next September, and we might not be so lucky.