interesting , even Scotland has a team but not England...
I'm not sure about other sports, but in team sports, like hockey, rugby, football. There are England, Scotland, Wales, and Northern Ireland teams.
There are many complex about sovereign state. There is team Great Britain in the Olympic, not England. Because GB is the member of IOC, others not. The athletes from Northern Ireland must choose to compete under GB or Ireland, because GB doesn't include Northern Ireland. United Kingdom is United Kingdom of Great Britain and Northern Ireland.
If you see the member in NORCECA, you will see more complex. Like US citizen, Puerto Rican, Guam people, and american Samoan, US virgin Islander They are American who use American passport, but last three can't elect US president. Guam and American Samoa are member of AVC.
In Kingdom of the Nertherlands, You will see Aruba, Curacao, Dutch St. Maarten,... in NORCECA competition. But, in Olympic, only Aruba, Curacao can compete. The others must compete under the Netherlands
You can see French Guyana compete in continental cup of beach volleyball. But, if they win, they can't compete in the Olympic.
Moreover, Macau and Hong Kong participate the Olympic, but when they win, the athletes stand for Chinese anthem.
The most complex one is Taiwan that can't use Taiwan, Chinese Taipei intead.