Jeremy Corbyn is facing a storm of criticism from Labour activists and MPs after suggesting he would press ahead with Brexit if the party won a snap general election.

In a sign that he is losing backing among overwhelmingly pro-remain Labour supporters, Corbyn was also accused of betraying the party membership by appearing reluctant to back the idea of supporting remain in a second referendum.

The first signs of a serious internal revolt from party members on the left, who helped propel him to the leadership, came after Corbyn gave an interview to the Guardian in which he suggested he thought Brexit should go ahead and said EU state-aid rules would prevent a Labour government intervening to support UK industries.

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His anti-EU tone drew immediate criticism from party supporters and members who had successfully persuaded the leadership to back the possibility of a second referendum at Labour’s annual conference in Liverpool in September.

Richard Brooks, a Labour member, activist and co-founder of For our Future’s Sake (FFS), a pro-remain youth and student-led organisation, said Corbyn risked losing the backing of young people as well as the mass Labour membership he had promised to empower. “Jeremy Corbyn is in danger of betraying and losing the support of millions of young people and students who very nearly propelled him to Downing Street last year, and whose support he needs if he is to ever to become prime minister.

“Students and young people will not forget or forgive politicians who sell them down the river by backing a Brexit that limits our life opportunities and makes us poorer,” he said.

Labour MPs who back remain said they were planning to issue a statement within days insisting that the leadership must take its lead from members over Brexit, and be ready to campaign for remain in a second referendum if the party cannot force a general election. Michael Chessum, who worked on Corbyn’s 2016 leadership campaign and served on Momentum’s first steering committee, said: “Real movements need internal democracy and leaderships that respect the mandates they are given. Jeremy has fought for decades for the right of members to decide policy, and that is why many of us fought for him so hard.

“It is beyond me why he would now seemingly take a stance so completely at odds with both the will of members and the mandate of party conference. If a left leadership is seen to thwart the will of members, this will do the left profound damage in the long run in Labour’s internal politics.”

Asked about a second referendum in his Guardian interview, Corbyn suggested his preference was to fight for a better Brexit deal than Theresa May had achieved. “It would be a matter for the party to decide what the policy would be; but my proposal at this moment is that we go forward, trying to get a customs union with the EU in which we would be able to be proper trading partners,” he said.

A Labour spokesman insisted Corbyn had not departed from the policy agreed in Liverpool, and was not opposed to a second referendum. “Jeremy Corbyn was restating Labour’s policy of rejecting Theresa May’s botched Brexit deal, supporting a jobs-first alternative, pushing for a general election and keeping all options on the table, including the option of a public vote,” the spokesman said.

The party’s deputy leader, Tom Watson, who has pushed for the party to hold open the option of a second referendum, stressed the need to take a lead from the membership on Brexit policy. “Labour’s programme for government is not yet determined because we have not yet written our manifesto. Our approach to Brexit will be determined after consulting members and taking heed of policy decided at conference.”

Pro-remain Labour MPs also tore into Corbyn. Pat McFadden, a former Labour business minister, said: “It would be a tragedy if Jeremy Corbyn facilitated Brexit and continued his lifelong hostility to the European Union on the basis of his views of the state-aid rules. There are plenty of EU member states with state-owned industries and with different tax and spend policies from those followed by the Tory government. It would not be the EU that would stop a Labour government regenerating the United Kingdom, but the economic damage brought about by Brexit that he may yet enable.”

Ilford North Labour MP Wes Streeting said: “Our members and voters are overwhelmingly pro-European. This lets them, and our country, down.”

Luciana Berger, the Labour MP for Liverpool Wavertree, said her party would never be forgiven if it facilitated Brexit, while former shadow business secretary Chuka Umunna described Corbyn’s remarks as “depressing”.

Meanwhile, support for a deal that would prevent the UK from signing its own trade agreements is gaining ground among some senior Labour and Tory MPs as a potential compromise that could end the deadlock. Frontbenchers and backbenchers in both parties believe signing up to a customs deal with the EU could be enough to ensure May’s deal wins a majority in the Commons next month. It would however anger hardline anti-EU Tories who would oppose any move to keep the UK tied to the EU’s economic system and prevent the UK signing trade deals post-Brexit.

The idea of keeping Britain in a permanent customs union was narrowly defeated in a vote in the summer, but some figures who voted against it then are now reconsidering as Britain’s formal EU exit looms. While the move would go a long way to solving some of the trade barriers created by a hard Brexit, it would also end the prospect of Britain striking its own trade deals with other countries.