The leader of backbench Conservative MPs has made a dramatic plea to warring cabinet ministers to unite at a crucial Chequers meeting this week – or risk a botched Brexit and a Jeremy Corbyn-led government.

Writing in the Observer, Sir Graham Brady, chairman of the 1922 committee, suggests that ministers should learn lessons in discipline from their backbench colleagues, after an extraordinary week of infighting at the top of government. Without an outbreak of unity at Chequers on Friday, he says the British people risk being sold short on Brexit and having to endure the “disaster” of a Labour government led by Corbyn.

“The danger of disunity at the top of the party is not just that it makes the prime minister’s job more difficult in negotiations with Brussels, and therefore puts at risk the good Brexit deal that is in reach,” Brady writes. “It also gives an impression of division to the country. Electorates these days are volatile, but one thing is certain: they do not vote for divided parties. They rejected decisively the divided Tory party in 1997. If we were to let Labour in again, it would be a disaster for this country.”

He adds: “It’s not just backbench Conservative MPs who expect ministers to pull together behind Theresa May: the great swathe of the electorate, which either voted Leave or voted Remain but recognises that a united team will achieve a better trading relationship for the future than a divided one, expects it too.”

His intervention follows a week in which cabinet ministers have openly disagreed about the Brexit process and also allowed disagreements over domestic policies and the overall direction of the party to burst into the open. The squabbles appear to be affecting Tory supporters’ views on who their next leader should be with Sajid Javid topping a poll for ConservativeHome - the first time the Home Secretary has done so since the website revived its monthly survey following the election.

With tensions rising before the Chequers showdown, where ministers are due to approve a final position on arrangements for customs and trade post-Brexit, it emerged on Saturday that the environment secretary, Michael Gove, had torn up a copy of May’s plan for a customs partnership with the EU at a meeting with other key figures in the Brexit debate.

Earlier in the week the health secretary, Jeremy Hunt, said that it was “completely inappropriate” for big businesses to make their views known on the dangers of a hard Brexit, only to be immediately slapped down by the business secretary, Greg Clark, who said their views should be respected and listened to. Ahead of the Chequers meeting, to be attended by all cabinet ministers, May has vowed to rule out any major concessions over freedom of movement after Britain leaves the EU, in a move that risks seriously limiting her ability to win a soft Brexit deal from Brussels.

Jeremy Hunt said it was ‘completely inappropriate’ for big businesses to talk about hard Brexit. Photograph: Mark Thomas/Rex

The prime minister will use the meeting to warn that time is running out to secure a deal and prevent the UK from crashing out of the bloc with no agreement in place.

Over recent days there have been suggestions that the government would consider rules limiting the right of EU nationals to come to Britain to those with a solid job offer. However, sources said Downing Street was “not in that market”.

“In the build-up to Chequers, there has been some speculation that the UK is willing to allow free movement to continue as part of the negotiations,” said the source. “The PM is clear that such a decision would not respect the will of the British people in the referendum.”

The latest draft of a white paper that will form the basis of the UK negotiating position is said to contain a commitment that Britain would keep its manufacturing regulations “substantially similar” to those used by Brussels. Senior Brexiters said they were happy with the wording, stating that there was nothing binding the UK to those regulations.

Senior sources in Brussels say, meanwhile, that May is using her political weakness as leverage in the Brexit talks, with British negotiators warning the EU of what could happen without a generous offer from the bloc on future trade.

The UK government has resorted to spelling out that the parliamentary arithmetic means that without a “precise and substantive” offer from the EU, it is likely that the prime minister will not be able to muster the votes in favour of the total agreement on the terms of the UK’s withdrawal.

EU sources say the tactics highlight just how desperate the UK government is and how precarious the negotiations have become. EU leaders at a summit in Brussels on Thursday and Friday expressed their growing anxiety at the cabinet divisions and the lack of progress, which have increased the chances of a no-deal outcome.