One of my classmates on my MSc (Durham) brought a cat over and adopted one. Frankly, I thought it was a bit nuts to do it for a year, but your situation is different as you'll be at least 3 years here.
I'm not going to lie, it's going to be tough. She was looking for a furnished place, which pretty much wasn't happening - students have a bad reputation as tenants in the first place, and most people won't want their furnishings subjected to cats with all the damage they potentially represent (pee, scratching, hair, etc.). You'll have a much easier time if you're looking to rent unfurnished, as the only risk for the landlord will be carpets, which should be covered by the damage deposit if your cats "misbehave". She ended up getting an unfurnished place, but it wasn't in the area she wanted. I think in the end she was glad to have a roof over her head at all - she was in a pet-friendly hotel for the first two weeks of term, having failed to secure a place prior to that. Definitely do your research in advance.