There's a biography of Lydia Thompson - http://www.amazon.com/Lydia-Thompson...dp/0415937663/ (preview at http://books.google.co.uk/books?hl=e...um=5&ct=result). She's also mentioned in quite a few other books too.

For more general history, you'll need to widen your search terms - try things like "Music Hall" or "Vaudeville "or "Variety Theatre" or "History of Cabaret". There are lots of histories of British music hall from the period you're interested in (like this one for instance), and lots of more general histories of cabaret (such as this and this). There will be specific country histories too, with books out there on the 'burlesque' theatre movements in America, Britain, France and Germany. Quick searches on Amazon have brought up tonnes and tonnes of interesting-looking tomes (this and this looks interesting for the history of strip-tease, and I'm sure Google Scholar, JSTOR and your local / university library will have loads more.

By "origins of burlesque" do you mean of burlesque cabaret acts, or do you mean the origins of girls doing fan dances in their knickers? The two histories converge at music hall.

Are you doing a university project?