I know this is what you said would happen but I strongly disagree. If we made a British team for football then we would have to make one for rugby, cricket and loads of other sports. In rugby, if all the british teams formed one team, then what would happen to the Six Nations and the Lions wouldn't be such a big thing. In Cricket, a lot of Welsh people play for England such as both of Jones and in the past Robert Croft. To make it even more internationall there are a few South Africans wth Pietersen and Straus (he was born there but has lived in England most of his life)
This probably doesn't make sense but even if football was played as Britain, who would play from the other nations?? We have a great defense (minus Neville) some quality Midfielders (gerrard and lampard cam 2nd and 3rd in European footballer of the year, and don't forget Beckham) and Rooney and Owen can be as good as anyone on their day, especially Rooney. Football would be a lot less patriotic and I don't think Scots, Welsh and Irish (sorry if I'm wrong Elly) would agree either. They wouldn't want a team of majority Englishmen representing them at such a passionate sport as football.
EDIT: I started before Elly wrote so I now see that she agrees.