In theory you could lose possession of the flat.
In practice, that is only likely to happen if you have a pet that is causing a nuisance to neighbours and if, when it gets as far as involving the courts, you refuse to get rid of the cat. Remember though that, as a leaseholder, it is likely that you are responsible for paying a share of communal costs as well as certain expenses specific to your property. It is quite possible that you could end up paying any legal costs to the management company even if things did not get as far as court.
Your best bet is to train your cat well and apologise profusely if it leaves any dead mice on neighbours doorsteps (pointing out, perhaps, that it is better to have a dead mouse outside than a live one inside!). You need to make sure that the cat doesn't "mark" its territory, make any mess outside or become noisy. Nutering often prevents these problems.
Dogs tend to be a far bigger nuisance than cats, budgies, fish and so on but leases tend to exclude all pets, just in case. If your cat is not going to be a nuisance, you should not worry, in my view, unless someone complains.