Moving to London with a dog

Hello!
I plan to move to London and would also like to take my dog with me. What I need is information about accomodation opportunities with a dog.

My dog, Báró is a sausage-dog, so he's small (about 6 kgs), he has a chip and passport. Is it hard to find a room for rent with a pet?
Do you know about prices?

Any information would be welcome - I couldn't find much via the internet yet.
Thank you in advance!

Cheers from Hungary (yet). :)