You're really going to struggle to find a rented house in surrey that allow dogs ... compared to other parts of the country what you are allowed to do in a rented property is very limiting ... generally, no smoking, no dogs, regular inspections, everything in the house must be EXACTLY is it was when you started the rental agreement as they will do anything to try and keep your deposit (video the place yourself as evidence - they're bastards!!!)
Good luck with your search
