AIBU to say, if you rent out your property, you shouldn't be able to stipulate 'No Pets, No DSS, No Sharers, No Smokers, and sometimes No Children (Although that may have changed)
If you are worried about damage then have extra deposit costs to cover.
After a marriage break down, I am having to rent and I am unable to take my 3 whippets with me as the landlord, doesn't allow pets. If fact its seems no one allows pets.