We own a two bedroom flat in Worthing, with a garden, and we TOTALLY allow pets.
We do not take an extra deposit.
We have not had any serious issues. No damage really. The dog of one couple did dig some holes in the garden, but we charged them out of their one month deposit to get it sorted, we got a gardener in, and they were fine with us doing that.
Dogs sometimes do that. So what? You just get it sorted out of the regular deposit.
I'm a pet friendly landlord.
Because we are pet friendly, we have never had an issue finding good tenants, quickly! We get so many people wanting the flat that it becomes hard to make a decision, because you have to let so many people down.
We have all hard wood floors, but even if we had carpets, we would be pet friendly!
Some toddlers can sometimes do just as much 'damage' as a dog or a cat, and they can make a lot of noise, and we allow THEM too! HA HA! If people allow kids, how is a dog any different?
I love animals, and the flat has a HUGE garden. It is perfect for a dog.
So, as an owner, I was pretty sad to see how many landlords were anti-animal.
Anyway, it is the same in NYC. If you have a dog and you are renting in NYC, you are going to have a VERY hard time finding a place! So, it is not just a UK thing.