Actually, the country/nation (regardless of what Brits will try to tell you, and who plays Rugby and Football/Soccer), is the United Kingdon of Great Britain and Northern Ireland...
So at the Olympics they represent their nation. At the Comm Games they don't.
The Olympic committee, and the UN use REAL countries, where as Comm Games needs more teams to compete...And in Football/Soccer the nations just want to compete separately, and are allowed to (they're not competing in the 2012 London Olympics because of the fear that if they play as a combined Britain there, FIFA will make them always combine).
And the password is for the United Kingdom of Great Britan and Northern Ireland.
Large parts of Scotland are actually campaigning for their independence. And there is always an issue, that the smaller 'nation states'/principalities Scotland, Wales, Northern Ireland etc, have their own parliarments for a fair chunk of their rules (as American and Australian states do too), but England doesn't. This means that issues effecting only England can be voted for by the Scottish representitives in the British parliament for instance.
David Cameron is the BRITISH Prime Minister, not the English PM. It is the BRITISH Army, not the English/Scottish etc Army. etc etc.
The interesting one is actually the Isle of Man (as people have mentioned, probably unknowingly with Cav). The Isle of Man is a self governing British dependency. The Isle of Man is not actually part of the United Kingdom, and so shoudn't REALLY compete with them at the Olympics etc...It is a grey area though, because they're also not technically a nation in their own right. Basically they're a British posession.
It also annoys me when the Olympics etc refer to the competing nation as "Great Britain". As this excludes Northern Ireland, and only includes the part of the UK on the main island. The "British Isles" are Ireland, Great Britain, and the channel islands etc. But "Great Britain" is the main island.