Scotland sing "Flower of Scotland" before rugby internationals, which is not the national anthem.
As an England fan it would seem more appropriate to me if all the home nations adopted the policy of singing a patriotic song of choice before games. It is clearly inappropriate for any team to sing "God Save the Queen", and "the Soldiers Song" throws up problems as has already been explained.
"Swing Low, Sweet Chariot" has been adopted as the anthem of English Rugby crowds, but it is hardly patriotic. Land of Hope and Glory might suit.