I think that's the point?
Analogous would be calling the USA “Texas”.
Calling the UK “Britain” is a much more direct comparison.
United States of America -> America
United Kingdom of Great Britain and Northern Ireland -> Britain
(United States of) America -> America
(Federal Republic of) Germany -> Germany
(United Kingdom of Great Britain and Northern) Ireland -> Ireland
Boris Johnson: "If I am ever asked on the streets of London, or in any other venue, public or private, to produce my ID card as evidence that I am who I say I am, when I have done nothing wrong and am simply ambling along and breathing God’s fresh air like any other freeborn Englishman..."
Rupert Brooke: "If I should die, think only this of me: That there's some corner of a foreign field That is for ever England."
Johnson is giving London as an example of a place in the UK. It is a very apposite example because it is where any power the police are given would be used most heavily (as stop and search is). He is using the the phrase "freeborn Englishman" to evoke associations with the use of the phrase that is far older than the UK. The phrase in its literal sense also excludes women and serfs and I do not think Johnson is aiming for that.
Brooke was writing a poem. He was evoking an effect and a particular sense of place and identify. "England" evokes different associations and and a different emotional response to "the united Kingdom". It is more local, and cosy, and has visual associations (the "English countryside" vs "the Scottish countryside" for example).
England is a country (part of Britain, together with Wales & Scotland)
The United Kingdom [of Great Britain and Northern Ireland], is an alliance of countries.
I'd hope that most citizens of the UK wouldn't regard these as interchangeable, and just because an Englishman waxes poetic about England doesn't mean he's unaware that it's part of the UK, etc.
No, it is not. The UK is ONE sovereign state/country, the rest are states/provinces/whatever, even tho some people living in this country might disagree and wish to separate themselves to become a full sovereign state.
Would have tried, perhaps.
But of course Dutch people don't really care what foreigners call the country, they can use whatever name they come up with it doesn't matter. Although it's nice that Germany gets it right. These kind of arguments speak to the fragile ego of some nations.