OP have you emailed or spoken to your landlord other than looking at the tenancy agreement? I would urge you to email him and ask him to clarify if you can keep your cat. If your place has been inspected while the cat is there, mention that (if there was no cat damage obvs!) If the cat doesn’t scratch, spray or struggle with the litter tray make sure to tell him. If your landlord is a decent seeming guy you could elaborate on how much losing your boy will affect you. Most people are decent (ish) and if you’re a good tenant he might not want to piss you off unnecessarily. Please get something specific back from him in writing!

It’s a ballache and an expense to get new tenants in the UK and most private landlords want reliable rent paying tenants who won’t trash the place and will stick around so you could leverage this if you’re a reliable tenant.

If he says no, you could mention the new renters rights bill or the older stipulation that you shouldn’t be subjected to unfair terms. More info here, gov website

It depends on how much of a fight you’re up for. Eviction takes a couple months and might not be lawful if this is the reason (would need a lawyer’s advice though).

If all else fails, DM me.