Properly speaking, the United Kingdom is the state including England, Scotland, Wales and Ireland/Northern Ireland, while Britain is England, Scotland and Wales (though often still used for the whole state). It can be a little jarring to read older authors and find they often use "England" for the state.
Was this simply a kind of English nationalism (invading and wiping out the other countries)? How and when did this usage change?
As a bonus question, what was the process like in other countries? (eg. usage of "Angleterre" vs "Royaume-Uni")
Yes indeed, 'England' seems to have been used for 'Britain' at least up to the second world war, well exemplified by Leo Amery's 1938 'Speak for England!' outburst in the House of Commons, implying Clement Atlee wasn't speaking for England for not declaring war on Germany immediately after the invasion of Poland. In Churchill's 1942 'End of the Beginning' speech he touches upon the English / British ambiguity, saying "The late M. Venizelos observed that in all her wars England -- he should have said Britain, of course -- always wins one battle -- the last."
I haven't read all of Krishan Kumar's 'The Making of English National Identity' (2003) yet but the bits I have read indicate that the shift happened at some point in the mid to late 20th century. He quotes (p. 3) A. J. P. Taylor who wrote thus in 1965:
"When the Oxford History of England was launched a generation ago, “England” was still an all-embracing word. It meant indiscriminately England and Wales; Great Britain; the United Kingdom; and even the British Empire. Foreigners used it as the name of a Great Power and indeed continue to do so. Bonar Law, a Scotch Canadian, was not ashamed to describe himself as “Prime Minister of England”, as Disraeli, a Jew by birth, had done before him . . . Now terms have become more rigorous. The use of “England” except for a geographic area brings protests, especially from the Scotch. They seek to impose “Britain” – the name of a Roman province which perished in the fifth century and which included none of Scotland nor, indeed, all of England. I never use this incorrect term . . . “Great Britain” is correct and has been since 1707."
Kumar then (p. 4) describes the change in terminology (to British) in academic work of the late 20th century, and gives as an example "A similar shift in consciousness is reflected in the decision to replace the old Pelican History of England by the Penguin History of Britain."