A British Isles team after 1921 is unlikely, after 1949, near impossible. The Republic of Ireland would never take part in a combined team, supposing FIFA developed the same as OTL.
If we don't look too much at the how, and say that a combined Great Britain team evolved from a touring squad of all the home nations, and the home nations championship faded from importance. Well, one difference would be the UK team would have won more than one world cup between 1950 and 1986. At that point a combined UK team would have been the best in the World by some distance. Even later, players like Southall, Strachan, McAllister, Speed, Giggs, Ramsey and, of course, Bale would have considerably strengthened the UK squad. The Republic of Ireland would also be much stronger, as many more English, Scottish, Welsh and Northern Irish OTL internationals who were eligible to play for them would be nowhere near selection for a GB team.
I suspect it would have strengthened UK identity to the extent that Scotland would never have had an independence vote TTL. Paradoxically, it may have led Irish Protestants to feel more Irish, as many of them may have opted to play for the Republic in order to play international football.