Political opponents said the Labour leader was “utterly pathetic” and “failing millions of working people” by continuing to argue that Britain should quit the trading bloc after Brexit.
The Scottish National Party (SNP) accused Labour of “siding with Tory extreme Brexiteers”.
It comes as Mr Corbyn faces renewed pressure over his Brexit stance after a new poll revealed 87 per cent of Labour members want the UK to stay in the single market and customs union.
The MP’s summit has been arranged by the SNP and is due to take place in the House of Commons on Tuesday. It will be attended by the Westminster leaders of the SNP, Liberal Democrats, Greens and Plaid Cymru and is designed to help coordinate cross-party efforts to keep the UK in the single market and customs union.
Mr Corbyn was invited to attend but declined, telling SNP Westminster leader Ian Blackford in a letter that he was wrong to suggest the single market “is a membership club”.
The Labour leader wrote: “Your proposed summit appears to be based on the flawed assumption that the single market is a membership club – it is not.
“We have consistently said that we are committed to negotiating to keep the benefits of the single market and securing the best possible deal for the whole of Britain, which protects the economy and the people of this country, whilst at the same time respecting the result of the referendum.
“Therefore, Labour will not attend your meeting.”
Labour has backed the Government’s decision to leave the single market and customs union but says it would negotiate some kind of access to the trading bloc.
In his letter, Mr Corbyn said he shared the SNP’s concerns about the Government’s “shambolic handling of Brexit negotiations” and promised Labour will work with other parties in Westminster “to hold this Government to account every step of the way”.
Mr Blackford criticised the response, saying: “It is unbelievable – and frankly, utterly pathetic – that on the single biggest issue facing the country Jeremy Corbyn has failed to show any leadership whatsoever, and is now rejecting this crucial chance to build a cross-party coalition in the national interest.
“His absence from this meeting is deeply disappointing but it is not surprising given his absence from the EU referendum campaign and the national debate on Brexit ever since.
“This is not the ‘straight talking, honest politics’ we were promised. Time is running out, and by sitting on the fence the Labour Party is failing millions of working people. Instead of protecting the jobs, incomes and rights that families depend upon, Jeremy Corbyn has chosen to stand by and allow hardline Tory and UKIP Brexiteers to have their way – beckoning the biggest threat to our economy in modern times.”
The other parties will leave an empty chair at the meeting for the Labour leader “should he come to his senses”, Mr Blackford added.
Mr Corbyn has refused to bow to calls from Labour members and MPs to change tack, as he tries to keep his party on side while retaining the support of voters in Northern heartlands.
He has previously said a Labour government would “strike a deal with the EU that “guarantees unimpeded access to the single market” after Brexit”.
However, with Brexit negotiations due to enter their second phase in March, the Labour leader is likely to face fresh calls to back full single market membership.
Last week the party’s former leader, Tony Blair, warned Labour risks becoming the “hand maiden to Brexit” unless it adopts a different approach.
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