Petition Private landlords to include clause for pets in tenancy

A PETITION TO ENCOURAGE PRIVATE LANDLORDS TO ACCEPT DOMESTIC PETS. Many private landlords are including a no pet policy in their tenancies, & due to the housing crisis and bedroom tax many are having to move into private properties and lose their beloved pets. We wish to propose a clause to be added in private tenancies to allow pets such as dogs or cats but that the owners are responsible for any damage the pet does to the property or garden and would be deducted from any deposit refund.
The animal rescues are full and many being taken free for bait on the web / abandoned / euthanised because good homes cannot be found for them. It is not fair to pets or the families to be torn apart when it is not necessary!!!