Diane Abbott has said she “intends to run and win” as Labour’s candidate in Hackney North and Stoke Newington following speculation she may choose to stand down.

Ms Abbott, who was this week told she would be allowed to stand for Labour after months of uncertainty, also denied she had been offered a seat in the House of Lords in the event she chose to retire.

In a post on social media, Ms Abbott said: “I have never been offered a seat in the Lords, and would not accept one if offered.

“I am the adopted Labour candidate for Hackney North and Stoke Newington. I intend to run and to win as Labour’s candidate.”

There have been questions over Ms Abbott’s future in the Labour Party ever since was suspended from the party last year for suggesting that Jewish, Irish and Traveller people experience prejudice rather than racism.

The comments, which she apologised for, sparked a long-running process which saw her sit as an Independent MP.

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Ms Abbott, the UK’s first female black MP, finally had the party whip restored earlier this week, theoretically paving the way for her to stand for Labour at the election.

However, her future appeared in doubt as some papers were briefed that she had been barred from standing for the party again.

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As a backlash against Ms Abbott’s exclusion gained momentum, Sir Keir Starmer initially said “no decision” had been taken regarding her future – before later going on to confirm that she would be “free” to stand for the party in the seat she has held for nearly 40 years.

His decision meant Labour’s ruling body, the National Executive Committee, was set to approve Ms Abbott’s candidacy at a crunch meeting on Tuesday.

But there have been growing rumours that, having been given the green light to stand for Labour, Ms Abbott was considering quitting politics altogether.

It was then reported in the Sunday Times that the veteran leftwinger was among a number of former Labour MPs who had been offered peerages in exchange for standing down to make way for Sir Keir’s allies in plum seats – something Ms Abbott has now denied had happened.

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Yvette Cooper, Labour’s shadow home secretary, also rejected the claim this morning, telling Sky News’s Sunday Morning With Trevor Phillips: “No party can do that, it’s not the way the system works.”

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She said there was a “whole process” for an independent committee to vet nominations to the Lords so it was not possible for Sir Keir, or any party leader, to promise anybody a seat.

The allegation came after Ms Abbott accused Sir Keir of “culling” Labour left-wingers after two potential candidates, Faiza Shaheen and Lloyd Russell-Moyle, were blocked from standing in Chingford and Woodford Green and Brighton Kemptown, respectively.

Former leader Jeremy Corbyn – who will now stand as an independent in the constituency of Islington North – also told Sky News Sir Keir was “clearly intervening” in a “purge” of left-wing candidates.

The Labour leader has denied blocking the left, saying his party had “fantastic candidates across the country” and he wanted the “highest quality candidates on the pitch for the task ahead”.