I'm so sorry you find yourself in this position.
Why do you think your landlord is going to find out? Is it inevitable that he/she will?
Do you want to stay in your flat? If you do, please don't give up too easily. Would your landlord really evict you because you kept a cat? If so he/she could use Section 8 but evicting someone is a big deal so they may not want to unless they want to evict you anyway and the cat is an excuse.
If you think they want to evict you cat or no cat, you could hang on in there - with the cat -and wait until the absolute end of the eviction process, possession orders, bailifs and all that, unless of course you don't want, or aren't eligible, for council housing.
Or you could just brazen it out, or lie, and say it's a stray or you've just got it for a couple of weeks.
I'm always a bit mystified by the No Cats in rented properties stipulation. You're allowed to have teenage boys with drum kits with friends that smoke weed, and young professionals who bring their friends back and play duf-duf duf music but one little cat that usually does a brilliant job of deterring rats and mice and ensures that the owner stays rather than moving every 2 years - well...
But if you do have to move, I think you'll find a lot of foster places/shelters are very full at the moment. The best thing would be to see if a kind cat-loving friend or acquaintance would be happy to look after you cat.