"It is thought that only 8 Carfields still survive."
Don't give up: usually the number of survivors is underestimated. And don't restrict yourself to the UK; Carfields were sold in Australia (particularly Queensland) in the 1920s. For example from the newspaper reports of the August 1927 Brisbane Show we get: "The C.C.M.'s other agency lines, the Rudge and Carfield-J.A.P., will also be shown in a full range of models."
Good luck!
Leon