Play are advertising the 10.1v, that is 10.9mm thick (v.s. 8.6mm) and has an 8MP rear camera (vs. 3MP), which has been out in Australia and parts of Europe for over a month now. Handtec and Clove are also advertising this model, based on their specs. Unfortunately they are all calling it the 10.1 (I don't know if that's what Samsung are calling this model in the UK or not).
Just another case of two tablets with very similar specs and very similar names that will lead to a lot of consumer confusion.
I've seen nothing recently to suggest that the UK will be getting the 'thin' Galaxy Tab 10.1 at all -- I'm expecting to have to import one from the US.