c.i.,
Very much looking forward to meeting you.
If we could predict the weather a month in advance, we'd be rich on the system! That's just the variable nature of it in Britain. Prepare for rain but not (usually) extreme cold. The wind may be more noticeable than the temperature, in that regard. You won't need shorts!
Here's a link to a show information site:
http://www.albemarle-london.com/news.html
I hope that helps. I haven't checked out anything other than Mamma Mia which is still running, but I'd certainly recommend that, if you like Abba's music.
KP