For a Labour MP accused of scheming to bring down the Prime Minister, it was not the most subtle venue: an Italian restaurant in Westminster, with a reputation for Guy Fawkes-style political plotting.

Louise Haigh was eating in Giovanni’s, a long-established family Italian restaurant in London’s Covent Garden, where Rishi Sunak’s political enemies in the Tory party used to meet to plot their rebellions.

Ms Haigh was dining two days before she recorded her recent appearance on BBC1’s Have I Got News For You, where she mounted a thinly veiled attack on Sir Keir Starmer for sacking her last year over mobile phone fraud.

As Frank Sinatra’s daughter, Tina, held court nearby – Sinatra: The Musical is preparing for a transfer to the West End – sources claimed that Ms Haigh’s group were heard discussing the Prime Minister’s leadership woes.

According to one diner, the former Transport Secretary was overheard claiming that she could do ‘a better job’ than Sir Keir. Last night, Ms Haigh strenuously denied making any such boast, telling The Mail on Sunday: ‘This is categorically untrue.’

However, the belief among Labour MPs that Sir Keir must be removed is now widespread.

One senior MP told this newspaper last week that Ms Haigh was being mentioned as a potential ‘stalking horse’ candidate to force a full-scale leadership challenge.

The Sheffield Heeley MP is considered to be one of the few challengers who could gain the necessary backing of 80 fellow Labour MPs to then trigger a formal leadership contest.

Last night her allies insisted that she had no such plans, despite that just two days after her night out at Giovanni’s, she used her BBC appearance to imply that Chancellor Rachel Reeves had received much fairer treatment from the PM over letting out her family home without a licence, than when she had to quit her Transport Secretary job after her 2014 fraud conviction became public last year.

It also emerged last week that Ms Haigh was taking up a key role in the Tribune group of soft-left Labour MPs.

Originally formed in the 1960s, Tribune will aim to spearhead opposition to any unpopular welfare cuts or other measures in this month’s Budget.

Last night, one senior MP suggested to this newspaper that such was Ms Haigh’s capacity to cause trouble for Sir Keir, that he would be well advised to bring her back into government. 

Judging from reports yesterday, however, such a move would do little to stem the wider plotting against the struggling PM.

According to one account, just yards from where Sir Keir was dining in the Commons last week, a group of despairing Labour MPs met to plot his demise in the hallowed

Smoking Room. One minister said: ‘We were there until late talking about who and the how and the when to replace him.’

As this newspaper revealed last week, Labour MPs are already privately assessing who should replace Sir Keir – with ex-Deputy PM Angela Rayner, Home Secretary Shabana Mahmood and Health Secretary Wes Streeting among the favourites.