Boris Johnson has said he hopes the EU will “show common sense” and agree a new Brexit deal, as No 10 refused to rule out scheduling an election in the first days after leaving the EU on 31 October if Johnson loses a confidence motion.

The prime minister said he still hoped to broker a compromise with the EU, days after it was reported Brussels officials now believed the UK was heading full tilt toward crashing out without a deal with no serious efforts being made to renegotiate.

“I’m sure there is compromise to be found and, as we’ve made clear, the backstop just doesn’t work for a proud democracy like the UK,” Johnson told the BBC. “We don’t want to go down that route. But there’s every possibility for the EU to show flexibility. There’s bags of time for them to do it and I’m confident they will.”

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He maintained the UK was working very hard to get a deal and “conversations are going on the whole time” but that the backstop would turn the UK into a satellite state.

“We need change on that. Once we get change on that, we’re at the races and I think there is a good deal to be done,” he said.

Asked whether there were any circumstances in which he would hold a general election before 31 October, Johnson dodged the question and said the public wanted MPs to honour the referendum result.

“I think the people of this country have had an election in 2015, they had a referendum in 2016, they had another election in 2017,” he said. “What they want to see now is the politicians they returned to Westminster – virtually all of whom promised to uphold that mandate to come out of the EU – what they want to do is see them do exactly that and leave the EU on October 31.”

Speculation about the timing of an autumn election is rife as Downing Street tries to figure out how to deal with the fallout if Tory rebels join with opposition parties to vote down the government.

Dominic Cummings, Johnson’s most senior aide and “assistant to the prime minister”, has told ministers and officials that the government is prepared to call an election to be held after 31 October and leave anyway if it loses a confidence vote.

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Leaving the EU, possibly without a deal, in the middle of an election while parliament is suspended for campaigning would be a highly controversial move. It would also be extremely risky for Johnson to lead the UK into an election in the middle of potential disruption to food supplies, travel and trade caused by a no-deal Brexit.

No 10 did not deny this could be a possible course of action in the event of losing a no-confidence vote, after the Spectator mooted the possible date of a post-Brexit election as 1 November and the FT reported it would happen in the “days after”.

Labour could hold a confidence motion in Johnson’s government as early as the first week of September to test whether he commands the support of the House of Commons. Should Johnson lose the vote, here would be a subsequent 14 days in which MPs could try to form an alternative government, but a general election would be triggered if they could not manage to do so.

Opponents of a no-deal Brexit would want an election to happen before 31 October in order to prevent the UK crashing out of the EU, but the Fixed-term Parliaments Act gives discretion to the incumbent prime minister to name a suitable polling day.

A cross-party group of MPs is working on plans to stop a no-deal Brexit either via legislative means or collapsing Johnson’s government, possibly sitting through the autumn recess in order to frustrate a no-deal exit.

David Lammy, a Labour MP opposed to a hard Brexit, has said the plan to hold an election after crashing out without a deal would be a “constitutional and democratic outrage that will impoverish millions” but he said a “flaw in Cummings’ plan to force us out during an election is we can refuse to back dissolution without a Brexit delay”.