Philip Hammond has become the most senior Conservative to signal that he might be prepared to back a second referendum, piling pressure on Tory leadership candidates backing no deal by warning that they could lose a vote of no confidence.

In a significant intervention, the chancellor said the only way of breaking the Brexit deadlock might be to put the decision back to the people, either through a general election or another referendum.

His comments suggest there could be growing openness among some soft Brexit Tories to a second referendum, meaning a majority for it in the House of Commons would not be impossible if Labour were to shift its position to unequivocally back a people’s vote.

“It will be a stain on parliament’s reputation if at the end we have to admit that we have been unable to agree how to discharge the [Brexit] mandate from the people,” Hammond told BBC Radio 4’s Today programme.

“But if we do get to the point when we have to admit that parliament can’t resolve this issue, then clearly it will have to be remitted back to the people. I am not sure the general election can resolve the question for the simple reason that both the main political parties are divided on the issues.”

Asked if he could support a second referendum, he said: “My strong preference would be for parliament to resolve this issue, but if parliament can’t resolve it, then parliament will have to decide how we remit it back to the people, whether it is in the form of a general election or a referendum.”

Hammond also hardened his previous warnings that he would be prepared to vote against his party’s government if the next Conservative leader decided to take the UK out of the EU without a deal. He told Sky News it was not a move he would make “lightly or enthusiastically”, but that “national interest trumps the party interest”.

Caroline Spelman, the Tory MP who worked with Labour’s Jack Dromey to pass a successful amendment in the House of Commons opposing no deal, said Hammond’s words should be heeded by leadership candidates.

Spelman, who has thrown her support behind Matt Hancock, an opponent of no deal, said: “You cannot be the party of economic competence and no deal – it doesn’t compute. And Philip [Hammond] was giving expression to that. He is speaking eminent economic sense.”

Rory Stewart, one of the more centrist candidates, has set himself against a no-deal Brexit but has ruled out backing a second referendum. Jeremy Hunt has also been clear that he does not want a no-deal departure from the EU, arguing that it would lead to a general election because the government would lose a no-confidence vote.

However, two leadership frontrunners, Boris Johnson and Dominic Raab, have both said that under their leadership the UK would leave the EU on 31 October, deal or no deal. Raab has even suggested he would be prepared to ignore any parliamentary moves to stop no deal.

Esther McVey, the hardest Brexit candidate, said she wanted a “clean break” no-deal Brexit without even an attempt to renegotiate the withdrawal agreement. Michael Gove, along with most of the other candidates in the Tory leadership contest, has said he would keep no deal on the table, but has not made leaving at the end of October a red line.

Hammond had previously indicated he would not run to be Tory leader, but hinted that he might change his mind if his views were not properly represented by another candidate. “My position is this: I have a very clear view about these things and I want to make sure my view is represented in this contest,” he said.

“Because my views are quite well known and have been expressed in quite uncompromising terms over a long period of time, I am, perhaps, quite a divisive figure. I would rather that the view I represent is presented in this contest by someone with, perhaps, a fresher face. As long as I feel the views I hold are properly represented, I won’t feel the need to take part.”

The chair of the influential business lobby group, the Confederation of British Industry (CBI), wrote to all the Conservative leadership candidates on Thursday night, asking them to commit to protecting business.

“The next prime minister can only claim the Conservatives are the party of business if they secure a Brexit deal that protects the economy, jobs and living standards,” wrote CBI chair Carolyn Fairbairn.

“Firms large and small are clear that leaving the EU with a deal is the best way forward. Short-term disruption and long-term damage to British competitiveness will be severe if we leave without one.”