The following was on Fiddle-L from Joseph Scott - a considerable expert on old American music. I'm sure he won't mind me quoting him here.
In the U.S. in the '20s through '40s, "skiffle" or "scuffle" (two ways of pronouncing the same word) described scuffling, i.e. busking music, music made usually on inexpensive instruments or imitation instruments and played in order to raise some money on the street, especially, or (more towards the '40s, best I can tell) at a rent party. It could be jazzy or non-jazzy. Sometimes the tunes were blues but they very often weren't. Music made by "ordinary folk" at home or to accompany dancers in rural areas tended to sound fairly different from skiffle, which by its nature had a professional, commercial component to it, but of course only to a degree, on a scale that did not aspire to be "high class." Jug bands tended to be skiffle bands or at least close, as did "tramp bands" and washboard bands. Skifflers tended to know standards people might want to hear such as "St. Louis Blues" and "Tiger Rag" (even if they didn't know them all _that_ well!) -- whatever would get tips into hats.
So Donegan and the other early (i.e. '50s) U.K. "skifflers" tapped into a real U.S. tradition. And presented it, imo, in a quite honest and straightforward way, all things considered, at a time when few people in the U.S. cared about skiffle any more.