Could a UK person tell us briefly about the Red list? What agency or organization compiles it?

Although Yellow-billed Cuckoos are supposedly common in my area (northeast Piedmont of North Carolina, USA,) I have never seen or heard one.

The Black-billed Cuckoo is supposed to be common where I was raised, in West Virginia. In spite of spending a huge amount of time in the woods, I never saw or heard one there either. The only Cuckoo I have ever seen or heard is the Mangrove Cuckoo, which we would occasionally see or hear back in the years I wintered in the Florida Keys.