Victoria and Albert Museum, London
Entry is free, and there's a reasonable amount of stuff on display. They update things occasionally, but not as often as I'd like ;) There quite a lot of modern fashion here, but decent historical stuff too. The rest of the museum is amazing, I could spend a whole day there, and there are costume gems mixed in with other exhibits, especially if you interested in dress from other cultures. Don't forget to stop at the book store, they've published at least 4 costume books illustrated with photos of the collection, and lots of post card available too.
The fashion Museum, Bath, Somerset
A whole museum dedicated to costume :) This place always lives up to my expectations, the items on display are gorgeous and varied so there's plenty to look at. They have special exhibits which change every 6 months or so so I can keep going back! If you're in bath, check out Jessies button shop, I always find some buttons I want!
Smaller collections:
Blandford Fashion Museum, Blandford Forum, Dorset
This place is fantastic, a house full to bursting with costumes, cost me about £3 to get in last time I went. One of the most fascinating things is the origins of the collection - it was all donated to one woman, who used to go round the country presenting a fashion show of the items - as in models walked down the runway wearing them while she talked about them. There a DVD of this and its worth getting. Pictures and video are allowed here.
Chertsey Museum, Chertsey, Surrey
This was todays discovery - free to get in, one room of costume and one room of accessories but the quality of the stuff on display was amazing! They were also very welcoming, and I plan on booking a study appointment to view some things up close. Again this was one womans collection, and the current display features around 20 wedding dresses from 1780 to 2001. They let me take pictures but I'm not allowed to post them here
So that my sharing done, anyone else got a hidden place they visit for costume eye candy?