John Bercow staying on as Speaker may not be enough to help parliament stop the UK leaving the EU without a deal at the end of October, according to one of the leading MPs trying to stop a hard Brexit.

Nick Boles, who helped with efforts to legislate against a no-deal Brexit at the end of March, warned it would be extremely difficult for parliament to make such a successful attempt again.

MPs have already voted against leaving the EU without a deal, but the Conservative leadership candidates Boris Johnson, Dominic Raab and Esther McVey have all said they would be prepared to leave the EU, deal or no deal, at the end of October.

MPs fighting against a hard Brexit cheered when Bercow told the Guardian on Tuesday that he would not vacate the Speaker’s chair while Brexit was unresolved. He also warned Tory leadership candidates that the idea they could sideline parliament in the Brexit debate was “unimaginable” and “for the birds”.

However, Boles, who resigned the Conservative whip over the failure of efforts to reach a Brexit compromise, said there were “extraordinary levels of complacency about the chances of MPs finding a way to stop no-deal Brexit on 31 October”, with people “blithely assuming MPs will find a way”.

He said stopping a “no-deal Brexit requires legislation to compel the government to seek an extension to article 50.

“For anyone other than the government to be able to move a new piece of legislation requires standing orders to be suspended.

“Suspending standing orders requires a motion or an amendment to that effect. Government controls the order paper so it can stop any motions that might be used in this way from being tabled.

“The Speaker can assert that parliament’s voice will be heard. No doubt it will. But voices alone aren’t enough. We need to pass a law. Neither the Speaker nor MPs can magic the opportunity to do so out of thin air.”

Challenged on whether the Speaker could defy convention to allow backbencher time to bring forward legislation, Boles said the idea was “wishful thinking”, because the Speaker had “no power to do that”.

On the suggestion that MPs could force a no-confidence vote in the government, he said a new Conservative prime minister could “avoid losing power after vote of no confidence by keeping negotiations going until EU Council on 17-18 October then prorogue parliament until 4 November”.

His comments reflect alarm among many MPs campaigning against a no-deal Brexit that a Eurosceptic prime minister could try to force the UK to leave without a deal regardless of parliament’s wishes.

Raab has even suggested he would be ready to ignore the will of parliament in order to do so, telling BBC One’s The Andrew Marr Show: “It’s very difficult for parliament now to legislate against a no deal, or in favour of a further extension, unless a resolute prime minister is willing to acquiesce in that – and I would not.”

The Institute for Government said there might be no decisive route left for parliament to block a no deal. However, some experts questioned whether there was the potential for an engaged Speaker to grant emergency motions or be more flexible in his interpretation of parliamentary convention to create opportunities for MPs to have their say.

The prospect of Bercow staying on longer despite widespread expectation he would depart this summer has infuriated Eurosceptic Conservative MPs, who believe he may try to defy convention to help the remain cause.

Bercow said on Tuesday he maintained strict impartiality and simply stood up for MPs’ rights.

Play Video 0:44 John Bercow: idea parliament could be sidelined in Brexit debate is 'for the birds' – video

But James Duddridge, a Conservative MP who previously tried to raise support for a no-confidence motion in the Speaker, said: “Bercow does not want to resolve Brexit. He wants to block it. He wants to veto the referendum result and will abuse the role of Speaker to advance his cause. He is even trying to comment on the leadership campaign. Pompous, egocentric, undemocratic and dishonourable.”

Another critic, Tory MP Andrew Bridgen, said: “We are going to face not only a parliament that is overwhelmingly remain but a partisan Speaker intent on overturning the democratic will of the British people expressed at the referendum to leave the European Union.”

The Tory Brexiter Mark Francois said: “As one vertically challenged MP to another, my sole advice to Speaker Bercow is: if you are going to stay on in these momentous times that’s fair enough, but it is important that all the players on the pitch retain confidence in the objectivity of the referee until the end of the match.”

Maria Miller, the chair of the women and equalities committee, weighed in, saying Bercow should not be allowed to stay on longer as Speaker in light of last October’s damning report about sexist bullying in parliament.

Bercow had faced calls to step down after the report by Laura Cox, but the pressure ebbed away after friends privately suggested he was planning to step aside in July.

“The Cox report was clear that the House of Commons needs a wholesale change in leadership to address an unacceptable culture of bullying and harassment,” Miller said.

“The Cox report specifically includes the Speaker in that recommendation, the most senior person in the House of Commons. No MP should stand by and allow the Speaker to continue in his post.”

Cox’s inquiry suggested that senior house staff, including Bercow, would not command the confidence to pursue necessary changes to the system for dealing with harassment and bullying.

Bercow told friends and other MPs he was planning to depart in summer 2019 but gave no public confirmation and then changed his mind after the UK failed to leave the EU in March.

Any move against Bercow is likely to be unsuccessful because he would be shored up by opposition parties and some Conservatives keen on his approach to ensuring parliament has a say on Brexit.

The Speaker won support from some Labour figures, including Barry Sheerman, who said he was delighted to learn Bercow had decided to “do his duty” and “see us through these troubled times”.

Andrew Adonis, the Labour peer and former cabinet minister, said: “John Bercow is absolutely right to stay in post until Brexit is resolved. He has enabled parliament and the people to take back control from a dictatorial and dangerous government. His duty is to remain.”