Calling England Britain and vice versa arose after the formation of the United Kingdom in 1707 when it was seen in England as an incorporating union, that Scotland had been taken over by England. Even Thomas Paine consistently referred to the "English" Parliament which of course had ceased to exist. In Victorian times, Disraeli's "One Nation" was England (this famous speech, referred to by Milliband recently can be read on line).
The approach is subtler now as the term "Anglo" is used ambiguously. We have the Anglo Irish agreement between the UK and Ireland but an Anglo Irish rugby match is between England and Ireland.
The Chambers dictionary is very clear in defining Anglo as unequivocally English.
No wonder foreigners are confused today and sometimes call the UK England when the UK government uses Anglo to describe themselves or, rather, their foreign agreements .. Anglo French, Anglo America etc.
Listening to the Westminster Parliament live, I don' know how many times an MP will refer to " ... the north east/west of this country" and they don't mean Scotland!
I don't think there is any malice in this, it's just foolish or maybe a wee bit arrogant in assuming we know they are talking about England, not Britain. Even Shakespeare had John of Gaunt referring to England as an island and that was before the Union!
As has been said before, this is not really a "nationalist" irritant but a question of correctness or even politeness.