We took two cats rescued in Cyprus back to the UK to rented accommodation in 2012, had no trouble, just searched before the planned move..found a place put down deposit flew back to Cyprus, packed up and sorted the cats flights with us ( passports were kept updated) and away we went....
We since rented a bigger place, again after asking, they allowed cats.... since renting from 2012- 2015 we've purchased a home in rural Wales, once we realised that we would be staying.
This link may help, but if you find a place, go see it and ask, you may be surprised how many put it, but would bend the rules if they approved of you.
http://www.letswithpets.org.ukOur place in Cyprus is rented out full time, the contract said no pets, the new tenants came along with a puppy, I relented, and I was right to do so, the contract now says one pet!
I think being with you, even when you're at work is better than not being with you....
But only you can decide...