Wes Streeting’s resignation has plunged Sir Keir Starmer’s premiership further into crisis, seemingly paving the way for a Labour leadership election.In his resignation letter, the now-former health secretary criticised the “drift” at the top of government and told the prime minister it was “clear” he would not lead Labour into the next election.Sir Keir is facing mounting pressure to stand down as five ministers have now resigned and dozens of Labour MPs call on him to quit or set out a timeline for his departure in the wake of the party’s disastrous performance at the local elections.As his woes deepen by the hour, one of the reasons he is still in place is that the path to No 10 will not be an easy one for any of his would-be challengers. From links to disgraced former Labour grandee Peter Mandelson to tax scandals, here we look at the potential difficulties each of the main contenders faces. Wes StreetingThe health secretary sensationally resigned from the cabinet on Thursday lunchtime with a searing criticism of the prime minister, in what was widely expected to mark the beginning of a leadership challenge.He blamed the “unprecedented” local elections results in part on “the unpopularity of this government”, adding: “There are many reasons we could point to: from individual mistakes on policy like the decision to cut the winter fuel allowance to the ‘island of strangers’ speech, all of which have left the country not knowing who we are or what we really stand for.”But he stopped short of announcing a bid for the top job, and allies have told The Independent that he won't be triggering a contest today, instead pointing to his letter, which called for a "broad" contest which includes "the best possible field of candidates".The statement suggests he could be in favour of including Greater Manchester mayor Andy Burnham in any leadership contest, in order to avoid accusations of purposely excluding the widely popular Labour mayor for self-serving reasons.Mr Streeting has never been shy about his ambition to become PM, and he is understood to have the backing of enough Labour MPs to launch a leadership bid, having recruited more than 81 MPs – the minimum required to trigger a leadership election. But launching a leadership challenge now could haunt him politically. Rishi Sunak’s resignation hastened Boris Johnson’s departure from No 10, but, although he became PM, Mr Sunak never quite escaped the reputation as the man who backstabbed his boss, and he faced accusations he was a traitor from Tory voters. While he is keen to avoid that fate, it is far from the only problem Mr Streeting faces. There is also his relationship with the disgraced Labour grandee Peter Mandelson. The now-former health secretary was forced to publish texts between the pair earlier this year, as the Mandelson scandal engulfed the government. Mr Streeting insists they were not close friends. Wes Streeting walks out of No 10 after attending a cabinet meeting (Reuters)Writing about the texts, he said that “contrary to what has been widely reported, I was not a close friend of Peter Mandelson, but I am not going to wash my hands of my actual association with him either”. Sir Keir was reportedly alerted to Mr Streeting’s intentions when a Downing Street staff member accidentally texted details of his bid, including the “five pillars” of his campaign and his “PFG”, meaning plan for government.He is a charismatic cabinet minister who is able to connect with the public. But his public popularity ratings are low, with only 13 per cent of voters thinking he’d do a better job than Sir Keir.But his position in the centre-right of the party could also prove a stumbling block to his ambitions. The next leader will not be chosen by the public but by Labour members, widely regarded as more leftwing that the general population.Andy BurnhamThe “King of the North” is popular among Labour MPs, party members and the general public. But he faces a major obstacle: he has no seat in Westminster – yet.Sir Keir infamously blocked a potential return earlier this year, barring him from standing in the Gorton and Denton by-election. But on Thursday, Makerfield MP Josh Simons announced he would stand aside, opening the door for Mr Burnham to stand in the by-election for the seat.Andy Burnham joins the PM on a school visit in the weeks ahead of local elections (PA)Obstacles remain, however – there is the problem of whether he would be able to stand, given most of the party’s powerful ruling body, the National Executive Council, voted with Sir Keir to prevent Mr Burnham from standing in Gorton and Denton.If he were elected MP, he would have to quit his role as mayor of Greater Manchester – triggering an election Labour fears it could lose amid the rise of Reform and the Greens. Allies say he has a plan to return as an MP, and his team is reported to have lined up an “impressive” candidate to replace him as mayor, potentially the reason to block him.But even if all these hurdles were cleared, he faces a tough challenge to win any seat at the moment. And the other parties, especially the Greens and Reform, will pile everything into a by-election to stop him. Angela RaynerRumours about Angela Rayner’s ambitions have been circling since she was forced to resign from Sir Keir’s cabinet last September, after it emerged that she had underpaid stamp duty on her Brighton flat. The row threatened to prevent her from entering No 10, until this week when she announced an HMRC investigation had cleared her of deliberate wrongdoing.Popular among MPs, who see her as a shrewd political operator, Ms Rayner is also on the soft left of the party and seen as more likely to get the votes of the party’s membership. Earlier this year, in what was widely seen as her clearest challenge to Sir Keir, she warned Labour was “running out of time” to deliver change and could not “go through the motions in the face of decline”.Angela Rayner is popular among Labour MPs but could her tax affairs be a stumbling block? (Getty)There were rumours of a joint bid with Mr Burnham after she met with the Greater Manchester mayor. That could boost her popularity, which has suffered since the tax scandal, with only 15 per cent of voters believing she’d do a better job than Sir Keir.Her tax affairs served to be her biggest stumbling block, with one Labour peer having told The Independent: “Labour cannot have a party leader who did not pay the correct tax – at the same time as it is putting up people’s taxes”. But on Thursday, the former deputy prime minister announced she was cleared of deliberate wrongdoing, in a decision that could pave the way for a potential leadership bid.In an interview with The Guardian, she did not rule out running in any Labour leadership race but said she would not “trigger” a contest.Al CarnsA surprise candidate is emerging to replace Sir Keir Starmer: new MPs among the 2024 cohort are pushing for former Royal Marines commander and now defence minister Al Carns to put his hat in the ring.Defence minister and former Royal Marines officer Al Carns is considered an outside bet (PA)One member of the 2024 intake told The Independent: “Why are we turning once again to the same familiar faces to solve problems they were involved in creating?“If we want to demonstrate genuine change to the public, we need a fresh face leading that change.“Members of the 2024 intake are still hopeful of persuading Al Carns to stand should there be a contest, and support for that view appears to be growing.”It is understood that a leadership team is being put together to support Mr Carns if he decides to make a move.Ed MilibandEd Miliband has emerged as an unexpected contender to be the prime minister, more than 10 years since he led the party to defeat in the 2015 general election.But in his time away from the leadership, the energy secretary has carved a niche for himself as the party’s top advocate for green energy and net zero.Surprisingly popular among young people, speculation has been rife that Mr Miliband is preparing an attempt to make a comeback as leader, with suggestions he could be the candidate from the party’s soft left.The recent Mandelson scandal has seen him grow increasingly critical of the government, telling broadcasters that he had raised concerns about the appointment with David Lammy at the time.A Miliband supporter told The Independent recently: “He has the energy and enthusiasm. He is loved by younger members of the party. He is a new man from when he was last leader.”Backers of the energy secretary say he also has the numbers to launch a bid but polling suggests only 13 per cent of voters think he’d do a better job than the current prime minister.