We had problems trying to find a rental house last year when we sold up and moved. The funny thing was I found that many agents said 'depends' - how many pets do you have and what breeds.....
Of course when I said we had 3 cats, a bullmastiff and a dogue de bordeaux, we found that the answer was a resounding no!
As if it makes as difference weather you have 1 pet or 2 or the size or them? You still need to tidy up after them!!!

Luckily we did eventually find a landlord who did not mind. Now we have had a couple of run ins with our letting agent because I have had to re-arrange their inspection and an electrical safety test twice!!! Although they have the right to enter the house even if I am not here, as long as they have given 24hours notice - they are EXTREMELY peeved that they CANT just enter unless i AM here - due to the fact that my male dog is extremely guarding of the house.....
I think they have realised that when we hand in our notice they are not going to be able to 'easily' show other prospective tennants around the house