The decision whether or not to allow pets is not always straight forward. Many good tenants including families and working couples have a cat or a dog. An outright "no pets" policy could mean missing out on what would otherwise be a really good tenant.
Many owners decide on a case by case basis. A small or medium size dog with a good reference of its own will often cause less damage than a boisterous child. A reference may sound over the top but will give some degree of assurance that the garden won't be dug up or the neighbours disturbed.
When allowing a pet, particularly dogs, it is a good idea to have a written agreement about the pet at the time of signing the tenancy agreement. Tenants need to agree to restrain their dog when inspections are done or tradesmen are sent to the property. Aggressive dogs are probably one of the biggest headaches for a landlord who permits pets.
Surprisingly even fish can cause damage with leaking tanks, so do think carefully before allowing pets.