There is no such team, I can assure anyone who remains in ignorance of this
The international teams representing the British Isles are England, Scotland, Northern Ireland, and Wales, corresponding to the regions with a separate national identity. Furthermore, people generally
do not support a team that represents another region merely because it is also British. Sporting rivalries here, which are essentially a patriotic expression of national identity, transcend international political boundaries.
There is a general principle, however, that if one is British, but not English, one supports any other team which is playing England regardless of nationality, this can be waived to some extent if England are doing particularly well in a competition in which one's own team is not participating, however. If the team is from one of the other British regions, one definitely supports that team against England, and possibly against other nations as well (on the general principle of sticking up for the underdog), unless there are league table considerations, or your own team has suffered a humiliating loss to them within recent memory.
As usual Wales didn't make it, so I have no-one to support really