Downing Street said allegations about Mr Bercow’s behaviour were “very concerning” and should be “investigated thoroughly”. It comes after former Commons clerk Lord Lisvane became the latest to complain and handed a dossier of allegations to the Parliamentary Commissioner for Standards.
But Mr Bercow denied the claims and accused the government of trying to stop him becoming a peer.
Mr Bercow said that since retiring it has “become increasingly obvious that the Government has no intention of honouring the centuries-old convention that a departing speaker is promptly elevated to the House of Lords”.
A government source pointed out that Mr Bercow, who stretched parliamentary rules during Brexit legislation, “wasn’t always a fan of convention”.
Labour leader Jeremy Corbyn is believed to have nominated him for a peerage after No 10 broke with tradition to deny him the honour when he quit last year.
Mrs Leadsom, who the former Speaker is accused of calling a “stupid woman”, said that no one in Parliament should be above the rules.
“As Leader of the Commons, I did a huge amount of work to bring into place a complaints procedure that would mean nobody, whoever they are, from employees of the house right the way to the Speaker of the Commons, could be allowed to get away with bullying, or harassment, or sexual harassment of any sort whatsoever,” she told LBC.
“That complaints procedure is in place. Anybody who is found guilty, whoever they are, should, in my view, not be able to skip from one House to the other.”
Lord Lisvane’s dossier is said to accuse Mr Bercow of having bullied and humiliated staff, including using inappropriate language.
Mr Bercow’s former private secretary Angus Sinclair previously told how he faced angry outbursts and was mimicked by Mr Bercow, who also smashed a phone on his desk.
Former Black Rod David Leakey, who was in charge of keeping order in the House of Lords, said at the time the ex-Speaker created a climate of “fear and intimidation”.
The Prime Minister’s official spokesman said parliamentary officials should deal with the latest complaint “fully and promptly”.
“These are very concerning allegations and they need to be investigated thoroughly,” he added.
Mr Bercow, whose autobiography, Unspeakable, will be published on February 6 with a major publicity blitz, “categorically” denied having ever bullied anyone.
He added: “Indeed, it has been suggested to me that the Government actively seeks to block any other attempt to nominate me for membership of the upper House.
“I have seen in the media that Lord Lisvane is formally complaining that I bullied staff. For the record, I categorically deny that I have ever bullied anyone, anywhere at any time.”