Finding a way around my "no pets" rental contract

I guess a little background is needed, I'm a huge cat lady, I've always loved and had cats, but about a year ago when I moved from London to live with my boyfriend I had to rehome my three cats as he rents privately and there are no pets allowed. This broke my heart, I lived with my mum as I'm her carer and she couldn't look after them like I could. I was devastated, it proved how much I loved my SO that I did this, the cats meant the world to me, but I knew it was for the best that they went to a family that could give them the love and attention they needed to be happy. Now, it's over a year since then and I'm broody as hell for another cat. We've since moved to a bigger flat but are renting from the same landlord and again, there's a no pet clause in our contract. We have two zebra finches that our landlord knows about and is fine with, but I want a pet that I can hold, play with and snuggle up to. I've been thinking of getting a cat (probably from a local sanctuary/shelter and telling our landlord that I found them outside in need of rescue. I know lying about this is wrong, but I figure she will be more willing to let me keep the cat if I say something like that.