Wales, Scotland, and England have their own teams (Northern Ireland contributes to the Irish team). The common explanation I’ve seen is that the nations have deep, distinct histories and cultures, but that doesn’t explain why, for example, India doesn’t get to send a team from each state despite India’s ethnic groups being even more diverse and distinct than those of the UK.
So what is the actual reason for Britain into three parts for the purpose of international sport but not other countries?
The UK has representation by 4 teams - England, Scotland, Wales, and Northern Ireland.
FIFA recognises that football originated in the UK and that “international” competition began with matches between the home nations. This unique status is enshrined in FIFA statute, giving the home nations separate status from other countries and territories.