Labour will support a fresh referendum on Brexit if Theresa May is unable to get a compromise exit deal through parliament, John McDonnell has said.

The shadow chancellor admitted it would be necessary “to go back to the people” if the prime minister rebuffs Jeremy Corbyn‘s proposal for a softer Brexit.

The Labour leader wrote to Ms May on Wednesday offering Labour’s support for a potential deal if five conditions were met, including a customs union with the EU and guarantees on workers’ rights.

That sparked an angry backlash from many Labour MPs, who want their party to support giving the public a Final Say referendum on Brexit.

But Mr McDonnell insisted Labour’s plan could secure a Commons majority and was now the only alternative to a fresh public vote.

The shadow chancellor told BBC Radio 4’s Today programme: “If Theresa May said ‘I’ll sign up to Labour’s deal’ and we went to parliament, I think we would have a secure parliamentary majority.

“But we’re at that stage now where we’re saying very clearly to everybody that people have looked over the edge of a no-deal Brexit and it could be catastrophic for our economy ... In the national interest we have got to come together to secure a compromise, and then if we can’t do that, well yes, we have to go back to the people.”

He added: “We’ve also said that, if there can’t be approval by the prime minister of our deal, if there can’t be agreement in parliament, we’ve kept on the table the prospect of going back to the people in a public vote.”

Asked to confirm that Labour had not ruled out supporting a fresh referendum, he replied: ”No, not at all.”

It comes after Mr Corbyn was forced to deny that his letter to Ms May torpedoed the possibility of Labour endorsing another public vote.

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Facing anger from MPs and party activists, he wrote to members to insist that the option remained on the table if Ms May rejects Labour’s alternative Brexit plan.

He said: “Labour can and must take a lead in bringing our country together.

“We are convinced that our sensible alternative, set out in the five demands in my letter, could both win the support of parliament and bring together those who voted Leave and Remain.”

He added: “Theresa May is unable to reach a sensible deal because it would split the Tories – and we will never vote for a bad Tory deal.