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?