I think that something being defined as 'of' a country would be defined as who currently owns it. Try telling the Brazilians that football's not their game.
Same goes for the English language in truth. Just because it was invented here doesn't mean it's emblematic of us any more.
My point re Engish v British is that after a certain point, our country is no longer England but Britain, so our achievements cannot be seperated out into the different regions of Britain. Engineering etc was made possible by the British economy, not the English one.
I would say again that something English in this context has to be primarily associated with England historically and currently. This is not true of football, or the language. Cricket is arguable, since it's mainly an English game in Britain (being not played much in the other parts) and it's really only played in the ex-empire countries as a consequence of British rule. I say arguable, since India for example support the game better than we do.