I think "Full English breakfast" is one of those terms which doesn't really have an absolute definition, since it can mean slightly different things to different people, and quite probably with regional variations thrown in as well.
I've always thought of black pudding as a northern thing, and certainly wouldn't assume it to be part of a full English breakfast where I came from. The good old British "banger," however, definitely has to be included!
I'd say that most people would expect a minimum of bacon, sausage, egg, tomatoes, and fried bread.