Gendarmes in the southwestern town of Samatan lowered their flag to half mast in a symbolic protest at pay, under-resourcing and what they see as inadequate support from the courts.
Councillor Andy Perkins, Labour group leader, said the first he was aware of the Conservatives' interest in flying the flag at half mast was at 11:00 BST when the funeral was well under way.
Councillor Matthew Riddle, deputy leader of the Conservative group in South Gloucestershire said it was "extraordinarily petty and disrespectful" that councillors with the other two parties would play politics and prevent the Union flag being flown at half-mast.
He said the flag at the Northern Ireland Assembly building should be flown at half-mast on the day of her funeral and books of condolence opened "across Northern Ireland".