For f* sake for the hard of hearing:
Landlords, you can no longer take a higher deposit than 5 weeks rent (6 if the tenancy is an extortionately high amount)
Tenants, we shouted until we were blue in the face that the tenants fee act which also capped deposits lobbied by Shelter would have this result.
There's no way in hell that 5 weeks rent will cover pet damage. We once had to replace every single carpet thanks to the tenants allowing the dog to shit everywhere and doing a piss poor job of cleaning it up. That cost 3 times their deposit ( and the deposit scheme gave it back to them!)
Not all tenants allow their pets to damage the property but there are enough that do, so afterwards that's another landlord who will no longer take the risk.
Your only option is to offer to pay a 'pet rent' which means that even if your pet is well behaved, you'll end up paying a premium. I'm sure that's just what Shelter realised what would happen, or as I suspect, they were so wrapped up in their 'fuck all landlords' campaign they totally failed to think through the consequences of their actions.
Let this be a warning. If you ban section 21 evictions ("no fault") it's going to make a lot of landlords decide to put their money elsewhere, so even less housing. Be careful for what you wish for.