Angry Labour MPs have attacked Jeremy Corbyn after his party chairman offered to quit for defying an order to back a fresh Brexit referendum – but was told to stay on.

The Labour leader stepped in to rescue Ian Lavery, a key ally, after he suggested he follow other frontbenchers by resigning for breaking the whip.

The show of support came as Mr Corbyn sparked a shadow cabinet battle by refusing to make a Final Say public vote a red line in his talks with Theresa May to strike a compromise over her defeated deal.

Ben Bradshaw, a pro-EU former minister, said allowing shadow cabinet members to “renege” on the pledge of a new referendum was a surefire way to “destroy the Labour Party”.

And Owen Smith, who was sacked last year for backing a new referendum, told The Independent: “Some might say Jeremy Corbyn has double standards about who he chooses to sack for expressing a view contrary to party policy and who he protects, even when they break the whip.”

It was the second time that Mr Lavery had broken ranks to abstain on a motion calling for any Brexit deal passed by MPs to be put to the public in another referendum.

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Two weeks ago, five Labour frontbenchers – Ruth Smeeth, Justin Madders, Yvonne Fovargue, Stephanie Peacock and Emma Lewell-Buck – did quit after breaking the whip over a second public vote.

On that occasion, Mr Corbyn’s political secretary is believed to have texted the rebels asking them to resign, which they subsequently did.

Mr Lavery, the MP for Ashington, in Northumbria, has not denied his offer to resign, telling Newcastle newspaper The Chronicle: “I never comment on private issues between myself and the leader of the party.”

The situation also triggered clashes at this week’s meeting of the shadow cabinet, where Diane Abbott, the shadow home secretary, and Angela Rayner, the shadow education secretary, spoke out.

A second Corbyn loyalist, Jon Trickett, the cabinet office minister, also defied the order to back the motion, which lost narrowly on Monday night. It is not known if he also offered to quit.

Neil Coyle, another pro-EU Labour backbencher, told the Politics Home website: “MPs from across the party, with divergent views on Europe, have resigned for not agreeing with the whip.

“Those who occupy places at the top do so with certain responsibilities. To ignore them is beyond disrespectful, but sets a precedent.”

Tom Watson, the deputy leader, said he was “disappointed” that Mr Lavery and Mr Trickett had failed to understand “what is expected of them”.

However, he added: “These are extraordinary times and we are a very forgiving bunch in the Labour Party.”