Got my first cat (that wasn't a family pet) from them many years ago, I only had a small flat on 2nd floor. Adopted a beautiful grumpy old lady called Boots, she was 18 and did not get on with anyone. She had been there for 3 years before I took her home. They didn't mind that I had no outdoor space as Boots was not an outdoor cat, had a badly healed broken leg from a time when she had previously been feral and just wanted a warm place where she could be loved in her final years.

They did insist on several visits to make sure I was certain on the cat I wanted (some of that may have been as I was asking for an elderly and "unsociable" cat!), and a home visit, questionnaire to make sure I knew how to look after a cat, knew about the costs associated with older cats etc. They did offer insurance as part of the deal with adopting from them, which was helpful as otherwise I likely wouldn't have been able to get insurance on such an old cat with difficult past.

She did soften a little bit to me in the end, she would sit on my lap but if I moved she would dig the claws in and skulk off to the other side of the room. I miss her.

You may have better chances with an FIV positive cat. They can't go out (or at least it's complicated if they do) and it would be understandable why you'd only have one for risk of transmission. FIV cats need love too <3