I want to post to say I'm delighted the way some of us are trying to make this forum a very useful place to refer to.
While I'm posting, I'd better try to add some possibly useful info myself!
No time to look which (if any!) shows are missing from the above list;
though here are some 'umbrella' URLs which might help fill some gaps in the meantime
(although I've noticed in the past that they've not always been quite up to date, especially re CAST info):
http://www.reallyuseful.com/rug/shows/ - Links for ALW shows
http://www.ukproductions.co.uk/ - Links for UKProductions shows (many UK National Tours)
http://www.kenwright.com/ - Links for Bill Kenwright's productions
And (further to Daniel K's list above):
http://www.flyingmusic.com/currentshows.shtml - Tours of Rat Pack & Thriller Live & That's Amore &c