It seems that it is common that standard tenancy contracts the estate agents prepare comes with the clause of no pets allowed, is it that they just don't want the trouble? I don't know. I think this is unfair.
Being an animal lover, my rental flat always welcome animals (never asked for extra deposit nor cleaning fee). I've always had good experiences with tenants with pets. For dog owners, I would just ask at the beginning if their dogs are toilet-trained and remind them to kindly keep the flat neat and clean. Every single time, I got my flat back in great conditions and no doggie smell even. For tenants who have cats, I have absolutely nothing to worry about, knowing cats use litter boxes.
In fact from my personal experience, tenants with pets tend to be more responsible and took better care of my apartment than those without pets.