Replace God Save the Queen with Land of Hope and Glory.
To play Land of Hope and Glory, a far more stirring anthem, at events (i.e The Olympics, when GB has a winning participent) where the Queen is not present. God Save the Queen, whilst being a tribute to our sovereign, is such a drab dirge in todays world.
Joe S commented
Or how about Jerusalem instead? I agree that God Save The Queen can be so dismal.