The Tory leadership contender Dominic Raab has said the possibility of sidelining parliament to force through Brexit should not be ruled out, as to do so would weaken the UK’s negotiating position in Brussels.

“I think it’s wrong to rule out any tool to make sure that we leave by the end of October,” Raab told BBC Radio 4’s Today programme, as the Conservative party reels from its disastrous results in the European election, in which Eurosceptic voters flocked to the Brexit party.

“The exam question in this contest is: who can be trusted to lead us out by the end of October and end this paralysing uncertainty,” he said.

Critics of the approach have warned that prorogation would involve the Queen in a constitutional crisis, because formally it is the monarch who ends a session of parliament.

Raab said it was unlikely to come to that because MPs’ powers to block a no-deal Brexit were limited. He said that if chosen as Tory leader he would return to Brussels with a “best, final offer” - including the removal of the Irish backstop – but insist there could be no further delay, and that the UK would be prepared to leave without a deal.

“I think anyone who is talking about delay or who is taking [World Trade Organization trade terms] off the table is having the perverse effect of weakening our negotiating position in Brussels. That’s the lesson of the last three years,” he said.

Quick Guide Tory party leadership contest Show What happens next in the Tory party leadership race? As she announced on 24 May, Theresa May stepped down formally as Conservative leader on Friday 7 June, although she remains in place as prime minister until her successor is chosen. In a Conservative leadership contest MPs hold a series of votes, in order to narrow down the initially crowded field to two leadership hopefuls, who go to a postal ballot of members.

How does the voting work? MPs choose one candidate, in a secret ballot held in a committee room in the House of Commons. The votes are tallied and the results announced on the same day. In the first round any candidate who won the support of less than 17 MPs was eliminated. In the second round anybody reaching less than 33 votes was eliminated. In subsequent rounds the bottom placed contender drops out until there are only two left. The party membership then chooses between them. When will the results be announced?

The postal ballot of members has begun, and the Tory party says it will announce the new prime minister on 23 July.. Photograph: Neil Hall/EPA

“It’s a test of nerve here and if candidates cannot stand up their resolve to lead us out by the end of October in a leadership contest, what chance would they have under the heat of the negotiations in Brussels?”

Raab said the Peterborough byelection, in which the Tories finished third, and the party’s drubbing in the European election, showed it was “devastating for the Conservatives if we don’t keep our promises on Brexit”.

He said: “What we can’t have is this paralysing uncertainty, bad for the economy, bad for trust in democracy, bad for the Conservatives – as we are seeing – of just going on and on with this prolonged torture of haggling with the EU when we haven’t got a deal in sight.”

The Commons Speaker, John Bercow, said on Thursday that it was “blindingly obvious” the new Conservative prime minister would not be able to suspend parliament to push through a no-deal Brexit.

“That is simply not going to happen. It is just so blindingly obvious that it almost doesn’t need to be stated, but apparently, it does and therefore I have done,” he told MPs.

Following Theresa May’s formal resignation as Tory leader on Friday, the starting gun has been fired in the race to succeed her. The nomination process will take place on Monday, with candidates requiring eight MPs to back them in order to enter the race, with the first round of voting on Thursday.