No 10 has made it clear that a new Conservative prime minister will be in place before MPs break up for the summer, meaning Boris Johnson is likely to face an immediate confidence vote in his premiership if he becomes leader.

Downing Street said it expects parliament to be sitting when the new prime minister is announced in late July, after Labour and some Tories raised concerns that the government was trying to avoid a test of its new leader’s ability to command a majority.

The statement means the new prime minister – whether that is Johnson, Michael Gove, Jeremy Hunt or another contender – is likely to face a swift challenge from Labour to prove they have the support of the House of Commons.

Theresa May has a working majority of just six with the support of the Democratic Unionist party. This is expected to fall to five after the results of Thursday’s byelection in Peterborough if Labour or the Brexit party win. This means just three Conservatives or DUP MPs would have to withhold their support for a prime minister to fail to form a government.

There are known to be a number of Conservative MPs who have deep reservations about serving under a prime minister who is prepared to leave the EU without a Brexit deal on 31 October, such as Johnson or Dominic Raab. However, several moderate Tories said they believed the whole party would, initially at least, get behind a new prime minister to give them a chance to avoid that outcome.

Mel Stride, the new leader of the House of Commons, who is key to Gove’s campaign to become prime minister, initially aroused suspicions about a ploy to put off a confidence vote when he refused to confirm when the recess would start.

He said it was “not necessarily” the case that the new Conservative leader would have to appear in front of parliament before MPs went off on holiday until the autumn.

However, the prime minister’s spokeswoman later clarified the government’s position, saying: “I fully expect that the house will ensure it is sitting when a new prime minister is appointed. Then it’s a matter for the house, after that, what activity or action it chooses to take.”

As a matter of constitutional propriety, May will only be able to resign as prime minister if she can tell the Queen that her successor commands a majority. A Downing Street spokesman said May would resign when “she says to the Queen that she is stepping aside and believes that someone else can command the confidence of the house”. Her spokesman said a vote does not need to take place for May to believe that the new leader has the confidence of the Commons.

Labour sources said they believed the government whips had been planning recess to start potentially as early as 19 July – almost a week earlier than last year – in a move that could have delayed a confidence vote in the new prime minister. The announcement of the winner of the Tory leadership contest is not being announced until the week of 22 July.

Peter Bone, a Conservative backbencher, told the Commons on Thursday that the new prime minister should face parliament straight away. “Parliament matters. It seems to me entirely proper that the new prime minister should face this house before any recess.

“If the government falls on a vote of confidence on a newly elected Conservative prime minister, I would expect the Conservative prime minister to take us to the country and return with a substantial majority. We should not be afraid of parliament. We should encourage it.”

Valerie Vaz, the shadow leader of the House of Commons, also called for MPs to have an immediate opportunity to test whether the new Conservative leader had a majority and warned Stride that he “holds democracy in his hands”.

“I have heard rumours that the house might rise on 19 July,” she said. “But I think there is a new timetable for the election of the Conservative leader. We need to make sure the house is not in recess when the new leader, and effectively the new prime minister, takes up his or her post.”

In response, Stride declined to name a date when the Commons will rise for recess.

The debate about a confidence vote came as the Tory leadership hopefuls were mired in a separate controversy over the role of parliament, after Raab suggested he could be prepared to suspend sitting in order to force through a no-deal Brexit against the wishes of MPs.

The idea caused outrage across the political spectrum, with John Bercow, the Speaker of the House of Commons, saying no Conservative prime minister would be able to pursue such an option.

“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.

Matt Hancock, another Tory leadership contender, called for all his rivals to rule out the possibility, arguing it undermined parliamentary democracy and risked a general election.

The home secretary, Sajid Javid, also came out strongly against the idea, saying: “I’m not into this proroguing parliament rubbish. It’s a complete nonsense. It’s anti-democratic and anti-British.”

Other contenders including Andrea Leadsom and Johnson also said they would not pursue such an option in order to take the UK out of the EU without a deal on 31 October.

Amid suggestions it could even be unconstitutional, Vazasked the government for clarity on whether prorogation to avoid a decision from parliament would be allowed.

Stride replied that prorogation was “ultimately in the gift of the Queen”, adding: “What I would say is, that I do think Her Majesty should be kept out of the politics of our parliament.

“I’m sure that will be a matter that will be at the forefront of those who toy with those decisions in the future.”

With May preparing to resign as Conservative leader on Friday, leading figures from the 1922 Committee of Tory backbenchers set out their rules to stop MPs from cheating in the battle to pick her successor.

They are making provisions for up to five rounds of voting starting on Thursday next week, with the candidate with the least support dropping out at each round. To stop any skulduggery, ballot papers will change colour each round, MPs will have to provide identification to stop them from voting twice, and they will be banned from photographing ballot papers.

After that process, which will be over by 20 June at the latest, a shortlist of two candidates will go into a run-off, the outcome of which will be decided by the party’s 160,000-strong membership.

Charles Walker, the acting joint chair of the 1922 Committee, said he would expect the final two candidates to remain in the race from that point onwards, amid rumours that some leading candidates were prepared to drop out rather than go through a head-to-head with Johnson.