Bercow actually overstepped his authority purely by admitting he was a remainer, that goes strictly against the rules of the speaker of the house.
“What conceivable moral force do the people’s elected representatives have in seeking to […] disregard a law enacted by Parliament?” (John Bercow, paraphrased)
I hate to break it to the Rt. Hon. Speaker of the House, Mr. John Bercow, but the moral force that he seems in question of is that ‘The Will of The People’ trumps ‘The Will of the House of Commons’ by a significant margin.