Hazel Blears regrets her timing - Courtesy Manchester Evening News
Hazel Blears will face a motion of no confidence next week at a meeting of her constituency Labour Party.
Her decision to quit as communities secretary, on the eve of the English council and European elections last week, has been widely criticised.
She has told the Manchester Evening News she regretted the timing of her departure and its effect on the party.
Labour MP Frank Field later said he hoped her apology would be accepted and she would return to high office.
Labour crashed to its lowest share of the vote at the European elections and lost control of four key councils.
Constituency sources have told the BBC it is unlikely the no confidence motion will succeed as she has the backing of her local party leadership.
But if the motion, which is understood to be backed by a number of local party branches, did succeed it would step up pressure on her to be deselected.
In an interview with the Manchester Evening News, Ms Blears - MP for Salford - said she regretted "enormously" the timing of her resignation - on the eve of the elections and after it emerged Jacqui Smith, the home secretary, was stepping down.
It was a stupid thing to do in retrospect but it was just putting a brave face on
"I genuinely thought I could go without it sparking off this huge firestorm," she said.
"In hindsight that judgment was wrong. I should have waited until after the election. The effect on the party is something I will live with for ever."
She was followed by another cabinet minister James Purnell - who resigned the next day telling Mr Brown to "stand aside" as leader for the sake of the party.
He told the BBC on Friday he had no regrets but would not make trouble for Mr Brown from the backbenches.
Ms Blears also said she regretted mocking Prime Minister Gordon Brown's YouTube video, which she described as "thoughtless" and wearing a badge saying "rocking the boat" as she quit.
It's fine for people like myself to forgive Hazel. But it's not me who she's got to apologise to
Lindsay Hoyle Labour MP for Chorley
She said she chose to wear the brooch after weeks of intense media pressure on her and her family over her expenses claims.
"At that point I just had enough, it was a stupid thing to do in retrospect but it was just putting a brave face on," she said.
But Brian Simpson, the Labour MEP for the north west of England told BBC Radio 4's PM programme he had been "annoyed" at Ms Blears' resignation just as Labour activists were out knocking on doors ahead of the elections.
"We were out there on the streets in tough times and to have that happen, it was a bit of a body blow," he said.
"I know there's a lot of very unhappy Labour Party members out there."
And Lindsay Hoyle, the Labour MP for Chorley, also told the BBC a lot of Labour activists were angry at the Salford MP.
He said: "It's fine for people like myself to forgive Hazel. But it's not me who she's got to apologise to. It's the people of Salford and all the candidates that were standing on election day and the activists who were knocking on the doors. It's the upset that's caused there."
He said some people blamed Ms Blears for a drop in the Labour vote and subsequent BNP victories in the region.
But Frank Field warned that it would be unwise to use the timing of her resignation as an excuse for Labour's bad results.
He also rejected the idea of examining her motives for expressing regret.
"If she said she's genuinely sorry, we should accept that. We shouldn't become these amateur psychiatrists, putting our sticky fingers in people's minds, trying to work out what they really believe."
He added: "She's a significant figure. She has read the times right about voting trends, more articulately than anybody else. And I hope she's back in a leadership role soon."
In the weeks before she quit Ms Blears had reportedly been unhappy with Mr Brown because he described her expenses actions as "totally unacceptable".
She had been accused of avoiding capital gains tax on the sale of a property she designated her "second home" with Commons officials.
But other cabinet ministers like Geoff Hoon and James Purnell were accused of similar actions, without a similar reprimand.
Before the expenses story broke, she annoyed many Labour members in an article she wrote for the Observer in which she wrote: "Promote your message via YouTube if you want to. But it is no substitute for knocking on doors or setting up a stall in the town centre."
Coming shortly after Mr Brown's much-criticised appearance on YouTube to promote his expenses proposals, it was interpreted as a thinly veiled attack on his leadership.
She told the Manchester Evening News on Friday: "It was thoughtless and it was hurtful and I apologised straightaway."
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