The shadow home secretary responded to a Twitter user who said he had so far backed Labour's position but was concerned by the momentum of the Greens and Liberal Democrats - who have backed a second referendum.
Ms Abbott said: "Like you I have supported Labour's Brexit strategy so far. But like you I am beginning to worry…”
Like you I have supported Labour’s Brexit strategy so far. But like you I am beginning to worry...— Diane Abbott (@HackneyAbbott) June 27, 2019
The admission from a long-time Corbyn ally suggests friction among those around the Labour leader, who has so far resisted calls to fully commit to a second referendum in any circumstances.
Mr Corbyn’s position flies in the face of several of his own MPs and thousands of party members, who say Labour should campaign for another vote - and back Remain.
Ms Abbott’s comments come after shadow chancellor John McDonnell reportedly described Labour’s Brexit policy as a “slow-moving car crash” at a shadow cabinet meeting.
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Emily Thornberry, the shadow foreign secretary, is also said to have fumed that “this is about leadership”, while shadow health secretary Jon Ashworth said Labour must have “the courage of our socialist convictions” and campaign to stay in the EU, according to The Sun.
Mr Corbyn has decided to delay his decision on whether to call for a so-called ‘People’s Vote’ for another two weeks so he can discuss the issue further.
Labour MP Neil Coyle – who backs another referendum – said: “Thousands have left the party as a result and thousands more voted for other parties in recent elections.
“The situation is unsustainable and risks harming Labour in future elections.”
Meanwhile, Brexit Secretary Steve Barclay has said he favours no-deal if the other choice was no Brexit.
Speaking in the Commons today, Mr Barclay said: "Between a choice between no deal and no Brexit - which a second referendum is a proxy for because, as a member for Don Valley (Caroline Flint) has said, a second referendum is actually a stop-Brexit referendum.”
In response to a question from Shadow Brexit minister Jenny Chapman, Mr Barclay added: "In answer to the question, between those two things I think no Brexit is worse than no deal.
"The point is no deal would be disruptive. I have been clear about that to colleagues on my own side.
"But the point is she has consistently voted against a deal and it is the deal that would have secured the interest of businesses.”
Boris Johnson has insisted he will deliver Brexit by October 31, “do or die”, but said the chances of no-deal were "a million-to-one against".