"I don't care about any team unless it's England."
Is it correct usage of unless? I wanted to mean in football world cup I just support England and I don't care about other team's winning or losing.
Yours is a correct usage of "unless." You can flip it around by saying "I only care about England's team."
"Unless" defines a condition to be tested that should evaluate to true or false. Therefore "the team is England" is the test, and only if it's true do you care about it.
"I don't care about any team except England" also works.