Shadow home secretary, Diane Abbott, wrote to two constituents this month pledging she would argue in favour of a referendum on the final Brexit deal, a policy that has previously been specifically ruled out by the party.

The Labour MP for Hackney North and Stoke Newington in London, wrote: “I will argue for the right of the electorate to vote on any deal that is finally agreed”, although when asked by the Guardian if her remarks were in line with Labour’s official no second referendum position she said her comments were “poorly worded”.

Her remarks were seized on by the leader of the Liberal Democrats, Vince Cable, who said: “It is really encouraging that such a senior member of the shadow cabinet should come out for the Liberal Democrat position of giving the public a vote on the final deal.”

Quick Guide What is the EU withdrawal bill? Show What is the EU withdrawal bill? The EU Withdrawal Bill – once known as the Great Repeal Bill – is going through the House of Commons to repeal the 1972 European Communities Act and transpose all existing EU legislation into domestic UK law, which will avoid a 'cliff-edge' change on the day after we leave the EU. Parts of the bill have been highly controversial, and MPs have tabled hundreds of amendments to try and change its wording, including a significant number of Conservative rebels. Some of the key controversies include its use of so-called Henry VIII powers, which will give government ministers the power to tweak the wording of laws to make sure they make sense in UK legislation - but those changes could take place without having to go through parliament. MPs have called this a "power grab" by the government. The government estimates around 800 to 1,000 measures called statutory instruments will be required to make sure the bill is applied correctly. Other concerns include the government's decision not to include the EU charter of fundamental rights in the law being transposed. Other amendments are attempts to affect the Brexit process, including legislating for a transitional period and giving MPs a binding meaningful vote on the deal secured by Theresa May, before the deal is finalised.

Hayley Dove, a constituent of Abbott’s who lives in Hackney, said she was surprised to receive the letter after emailing her MP on 6 November asking her to support amendments to the EU withdrawal bill.

The amendments highlighted by Dove included one cross-party amendment that would give MPs a meaningful vote on the final deal, as well as several Lib Dem amendments, including one that provides for a referendum on the deal before the UK leaves the EU.

“I think it’s absurd she has responded in this manner,” Dove said. “If she does believe what she says in this letter then she should say so publicly and make it really clear.”

Diane Abbott’s letter to her constituent, Hayley Dove. Photograph: Hayley

Les Kelly, 52, a constituent from Stoke Newington, also received the same letter on 22 November, a week after emailing the MP from a petition site about the EU withdrawal bill. “Like a lot of people in the constituency, I’m very concerned about Brexit. I was really surprised to see it,” he said.

In reply, Abbott said: “There is no important story here, just a poorly worded standard letter that was sent out. There is no difference at all between my position and official Labour party policy.”

Corbyn has ruled out Labour offering a referendum on the final deal during the 2017 general election. “A second referendum is not our policy and it won’t be in our manifesto,” a spokesman said during the campaign.

Abbott, who was a strong supporter of remain during the referendum, has signalled in the past she still has some discomfort with leaving the EU, but has argued the party needs to respect the democratic verdict.

The shadow home secretary missed one of the parliamentary votes to trigger article 50 but then voted for the bill at its third reading.

In her letter to the constituents, Abbott said the Labour party was “committed to retaining the best deal for all” in the Brexit negotiations. “I want to reassure you I am fully focused on defending the interest of the UK and I agree there should be parliamentary scrutiny and transparency,” it said.

The replies were shared with local Lib Dem activists who in turn passed the messages to the party hierarchy. Cable, whose party has called repeatedly for a referendum on the final deal to give the public the option of remaining in the EU, said he hoped the shadow home secretary would prevail in her arguments.

“It is really encouraging that such a senior member of the shadow cabinet should come out for the Liberal Democrat position of giving the public a vote on the final deal,” he said. “I call on them to confirm that they back Diane Abbott’s new position. I also look forward to working with Diane Abbott to give the people the chance to vote for an exit from Brexit.

“If the progressive parties did work together to give the public a say on the final deal, we could, even at this late hour, still stop Brexit.”