During the Commonwealth Games, England, Ireland, Wales, and Scotland all have their own national anthem. Why is it that when playing football, all the other countries play their national anthem, but England plays "God Save the Queen", which is the national anthem of Great Britain? Why does the England football not have their own anthem?
The more interesting question is why England plays something other than "God Save the Queen" at the Commonwealth games, which they have since 2010.
To the extent England has a national anthem, it is God Save the Queen; see this article for example:
National song of England is 'God Save the Queen', the British National Anthem. It is usually sung before England's football matches as well as some other sporting events. England's Rugby team, however, have unofficially adopted Land of Hope and Glory which is sung before rugby matches.
However, in 2010, they held a poll as to which song to sing at the Commonwealth games specifically:
At the Commonwealth Games, however, Team England decided to put the question out to the public. In a 2010 poll, voters chose between the three potential anthems to put ‘Jerusalem’ in first place with 52 percent of the vote, followed by ‘Land of Hope and Glory’ with 32 percent and ‘God Save the Queen’ with 12 percent.
In general, each organization can choose what is played for it - hence why England has some variety, as different organizations choose differently.