As a landlord, I wouldn't necessarily have a problem with pets - even though the agreement says 'no pets without consent'. One of our current tenants has a dog and it's not a problem.
The only point you should be aware of is some possible extra cleaning costs at the end of your tenancy. Pets, both cats and dogs, do create more dirt than would otherwise be the case (pet owners don't always notice this themselves) and either you would have to do extra cleaning or the landlord would (and would charge you for it). So long as youre aware of this I wouldn't see a problem.
It shouldn't mean an increase in rent but some landlords might like extra on the deposit to cover any extra cleaning or damage. It might even be worth offering this if the landlord hesitates about giving consent.
If you've rented previously, with the cat, then you should be able to get a reference from your previous landlord that the cat didn't cause a problem.