There is no national databse in the UK but our sister site Cat Chat will allow rescues to post cats that need homes on there. Thats theiir main purpose.
They are a registered charity and also have unpaid volunteers who will post pictures and info for a rescue.
It does have to be a bonafide rescue though and if you go to
www.catchat.org there is a place for rescues to ask for a form to complete to get things started.
All of us who started with Purrs came from CC when it closed its forum for a while but the rescue side never closes and if you click anywhere on the UK map they have and just pick on a rescue you will see how it works.