I've had very under-whelming experiences with animal rescues in the Uk.
20 years ago I wanted to adopt an adult cat (I'd never had a cat before) I was privately renting (very secure was family friend) until I bought my own home with the next year or so.
I was turned down by the local RSPCA for all the cats I wanted, an absolute no because of my housing circumstances, but they were happy for me to have a kitten or an extremely traumatised & aggressive cat (that presumably no one wanted).
I'm the end I took to FB and rehomed an unwanted cat from someone 150miles away - the cat lived with me for 18 years.
My next experiences have been with the local dogs trust. I'm in a fairly nice area, the dogs they have are mostly huskies types & dogs imported from Ireland. They turned me and DH down for some reason 15 years ago, I can't remember what, probably because we were honest and said yes likely the dog would be left alone at home for more than 4 hours in their lifetime as although one of us could WFH & both could take the dog to work with us we didn't realise how strict they were going to be because we were experienced dog owners with own home/garden/no kids etc.
All their dogs were horrible, lots and lots of behaviour issues (not the Irish dogs as they were unknowns/strays) and not breeds we ever would have considered due to breed traits let alone the additional behaviour issues.
We bought a puppy instead - this was DH first choice but I wanted to get a rescue and unfortunately we weren't allowed.
When I got divorced and lost the dog I just went for a rescue from abroad. She is perfect, been with me 6 years, I'd get another that way when she goes unless I can find a private genuine re-home from the Uk