Great Britain, as others have pointed out has its meaning dervied in size. We became Great Britain after the Acts of Union with Scotland.
Britain then became great through its navy. It facilitated existing trade routes, and then became a mean through which Britain could impose its own trading terms. Not long after follo0wed gunboat diplomacy, and then an empire.
This conventional view is then expanded by Britain's very self interested approach to national security. Having conquered internally and created the construct of Great Britain (OK, Ireland has remained a thorn in the side), the key then was to protect the borders, which as an island are significfant (c.15% of Europe's coastline). So, it has been Britain's policy to ensure that whichever mainland European nation develops too much power (mainly France, and also Germany now and again and more recently). With the construct of the EU (and its previous incarnations) it has been key to find our place in it in order to maintain this approach.
Having built the largest empire in modern times, it was, as is the way with all empires (go back and look at the Chinese empires onwards), it finally came to an end with the creation of the Radcliffe Line and with it Pakistan. Since August 1947, Britain has no longer been "great" in the sense of its primacy as a self interested expansionist capitalist nation state (whilst retaining the oddity of stateless nations within), and so has struggled with its inevitable decline.
This decline – and don't think for a minute this is a nation in any other state – has been ameliorated by certain key peaks – the establishment of the welfare state, culture imperialism (though we are deluded if we think that competes in any way with the USA during the C20th), and an enlightened (though, of course, entirely financially driven – we needed a workforce) attitude to inward economic migration has, in combination with the historic desire to make as much cash as possible, meant that we attract more apparent international attention than a nationof 60 million inhabitants might otherwise expect.
The cultural aspect is probably the most significant since the middle of the C20th, and Britain's influence was most of all through its demand that so much of its recent empire speak English. The stroke of luck was the USA's own influence – pop music and film lead here, the former containing our own contribution – has cemented that. Much of that is because we have a very relaxed attitude to the development of the language, allowing it to take on all it needs from all others (e.g. bungalow, pyjamas, cul-de-sac, graphic) without being too fussy like french.
Our time has passed, and it pains us to watch the rise of China and India, but we have to accept that our greatness lies not in what we continue to do on a macro level now (I agree about individual things), but what we did for 500 years up to 1947.
