It depends on wether the world governing body of a sport recognises the home nations, or recognises the UK as a single country. FIFA, (the football guys) recognise 4 seperate nations, as they are registered with FIFA as such. In athletics, Great Britain is registered with the IOC and is recognised as such. Consequently, there is no UK football team playing at the Olympics. The same pettern pretty much follows for all other sports, but if anyone can tell me otherwise, i'd love to hear it. There are times when the home nations put their differences aside and gang up to take on the world, such as the British Lions Rugby Union team, who make an almost annual pilgrimage to somewhere in the world, just to prove the Brits are best at rugby. Although they rae not an 'official' team, just a touring side. There is also the consideration that the countries are split up sometimes because some of the host nations do not play a particular sport. For example, there is a Great Britain Rugby League team, but that is more to do with the fact that by and large, Rugby League is not played in Scotland, Wales or Ireland, they stick to Rugby Union mostly. On the flip side, there is Cricket, where Scotland, Wales and Ireland don't play much either, but England has reserved the right to call the team England, even though Scottish players have played for the England side in the past, due to Scotland not having a Test Cricket team. As you can see, there are reasons why it happens, but I think the biggest reason is national pride. Scotsmen (me), Welshmen, Irishmen and Englishmen are very different people who are all very proud of their individual identities and wish to be seen as such.

Very simply it is the British Athletics Association but in other sports is the Scottish Football Assoc, Football Assoc (England). English cricket is actually England and Wales. Same with rugby etc