Hi Ferret

Hows it going. Findind properties to rent that allows pets....what a challenge. I'vedone it loads. It is hard. In Leeds unfortunately I cant assist as I am now looking to rent my property specifically to pet owners............and I don't know where to find them. I have recently come across a website, you might have heard of it. Pet Friendly Rentals - pets welcome property & UK holiday accommodation to rent
I did a general search for Leeds but didn't find anything, that said there is a Tennants section so maybe you could place your own ad......not sure. There is also a site called Property Rent - Letmatch | House rent, Apartment rent, flat rent, free property advertising, property let, house let, flat let, room to rent, UK Nationwide rentals, free letting advertising, free rental advertising, 100% free for landlords and lettin and I'm almost certain you could place an add here.
Good luck mate and kinow that there are land lords that will rent their property to pet owners.........you just have to seek us out.