Petition Being able to have animals when private renting

I would like a new law to come in place for people that private rent to be able to have pets without having to ask the landlord.
In most cases you pay a deposit that is kept in a government scheme that you get back if there is no damages.
So therefore, if your animal damages the property then you should be made to pay for it.
I just think it's so unfair that my children and a lot of children out there are growing up without pets.
I help out in an animal rescue centre and it makes me me mad that we have a lovely 3 bed house with a lovely garden and we cannot give one of them a home.
Why can council tenants have pets and pay less and us that private rent ( because nobody can afford the deposit to buy!) Can not.
I'm not talking a house full of pets, just 1 pet.
Please can this be looked into.

Many thanks

Miss Francis