Dave, RE made quite good bikes (of their type) in the early post WW2 period. Some fairly decent schoolboy sports bikes, in the same market as Sun, Carlton, Dawes and others.
I remember (1955) a visit from the RE representative, who brought round a new model for me to try. When I told him I thought it was "lively and responsive" he just didn't know what I meant, he could only apply that to their motorcycles.
I hope there are some people on here who know what I mean.