Philip Hammond has told Boris Johnson that leaving the EU without a deal would be a betrayal of the referendum result, as the former chancellor led a group of 20 Conservatives making clear their opposition to crashing out on 31 October.

In a sign that some Tory MPs are determined to block a no-deal Brexit, Hammond appeared to blame Dominic Cummings, Johnson’s senior adviser, for making demands for a new deal that the EU “cannot and will not accede to”.

Writing in the Times, he said: “The hardliners may make the most noise but they are not the most numerous. Most people in this country want to see us leave in a smooth and orderly fashion that will not disrupt lives, cost jobs or diminish living standards, whether they voted leave or remain in 2016. No deal would be a betrayal of the 2016 referendum result. It must not happen.”

In an apparent swipe at Cummings, he said: “The unelected people who pull the strings of this government know that this is a demand the EU cannot, and will not, accede to. Not just because they will be stubborn in their defence of the single market (although they will), but because the fragility of their own coalition of 27 means any attempt on their side to reopen the package would see their unity collapse. They will not take that chance and the smart people in Whitehall know it.”

A senior Downing Street source said: “Philip Hammond actively undermined the government’s negotiating position by frustrating and obstructing preparation to leave the EU. Everyone knows that the ex-chancellor’s real objective was to cancel the referendum result.”

The former chancellor is leading a group of 20 Tories, including seven former cabinet ministers, who have written to Johnson accusing him of setting the bar too high in negotiations with the EU to have a hope of getting changes to a deal.

Signed by Greg Clark, David Gauke, Rory Stewart and others, the letter says: “We are alarmed by the ‘red lines’ you have drawn which, on the face of it, appear to eliminate the chance of reaching agreement with the EU”.

The intervention is a sign that Tories opposed to a no-deal Brexit are prepared to vote with opposition parties to prevent Johnson taking the UK out of the EU on 31 October without a deal.

At the same time, John Bercow, the Speaker of the House of Commons, vowed at an Edinburgh festival fringe event to fight attempts to sideline parliament “with every breath in my body”. He said he would insist on the right of parliament to continue to sit and debate.

Cummings, the architect of the Vote Leave campaign, has told staff in No 10 that the rebels are too late to stop a no-deal Brexit, as the prime minister could simply push it through on 31 October and hold an election afterwards.

However, his opponents are incensed by the idea that parliament could be sidelined and have been working over the summer on ways to prevent that happening. These include a confidence vote to replace Johnson as prime minister with a temporary government or passing a law to force him to extend article 50.

Johnson insists that he wants a deal with the EU but only one that does not include the “undemocratic backstop” – the insurance mechanism to stop a hard border on the island of Ireland that Brussels says must be a part of the deal.

Since taking office, the prime minster has ramped up preparations for leaving without a deal in a move to convince the EU he is serious about leaving on 31 October regardless of whether the UK has a withdrawal agreement in place.