Can't miss an opportunity to plug my home town ... although this is more a street arts festival:

Big in Falkirk

Of course, the best one to see is in Edinburgh, but i guess you may have heard of that one already

Have a look at Guardian.co.uk and search on Arts Festivals 2007. There's the full list (loads!). I hope you have lots of time.

How about this one: http://www.dgartsfestival.org.uk/ in beautiful Dumfries & Galloway?

I should have said - I've done Edinburgh a few times already. Dumfries & Galloway sounds nice, I'll consider that one.

rpbristol I checked out the Guardian website - couldn't get a whole list but the search did give this page: travel.guardian.co.uk/nwda/story/0,,1857389,00.html

I hadn't heard of the Manchester International Festival until now - but then it is the first one they're doing - but that looks good too. Thanks for pointing me in that direction!

As you are obviously considering other times of the year other than June and July how about the Pittenweem Arts Festival? It starts on 4th August.
http://www.pittenweemartsfestival.co.uk/pittenweem.html