Speaking as a resident of the Celtic Fringe I totally understand the annoyance that English teams use the UK national anthem.
GSTK is a slow dirge that drips with subservience, so leave it for UK State stuff.
If England had to use one of the "established" other anthems, it should be Land Of Hope And Glory. Banger.
Personally, I'd rather it was Friggin' In The Riggin' by The Sex Pistols, though.