Why do they compete in the Olympics as the UK, but they compete in the World Cup as England?

Which one is an actual country?

No idea about why they chose to have a common Olympic committee, but in the old days of soccer they all started separate national teams (the first international soccer games were between England and Scotland) and joined FIFA as separate national organizations.

The Football Association (England)
Scottish Football Assocation
Irish Football Association (Northern Ireland, not to be confused with the Football Association of Ireland which is for the Republic of Ireland)
Football Association of Wales

Now, in London 2012 it has been stated that a team will represent GB in the soccer tournament. The non-English associations are against this because they think it will threaten their independence in FIFA, so it's possible the GB team might only have Englishmen.

thanks!