One recent morning at Mount Pleasant, in London, the largest mail sorting office in Europe, workers gathered to listen to Jeremy Corbyn. Addressing them from the top of a car park, he reaffirmed his support for a “publicly run” Royal Mail (the state’s remaining 14 per cent stake was sold in October) and vowed to stage an ­opposition-day debate in parliament on postal services. “It’s the busiest postal day of the year [14 December]. We’ve got everything to be happy about!” he cried.

The Labour leader has reached the point that many of his detractors thought he would not. When he became the front-runner in the Labour leadership election with the support of the Communication Workers Union, among others, several MPs privately predicted that he would be “gone before Christmas”. It was said that Corbyn, who won with the backing of just 14 of his parliamentary colleagues, would be unable to form a shadow ministerial team and would face a “coup” within weeks.

Speculation about a coup started again in advance of the Oldham West and Royton by-election on 4 December. When Ukip vowed to turn the contest into a referendum on Corbyn, it began to be feared that Labour’s 14,738 majority would be reduced dramatically. But, against expectations, the party’s vote share rose from 54.8 per cent to 62.1 per cent even as its majority fell to 10,722. Labour disagreed about why: Corbyn’s supporters cited the result as an endorsement of his anti-austerity programme, his opponents emphasised the local popularity of the candidate, Jim McMahon, who had been leader of Oldham Council. But they agreed about one consequence: the result secured Corbyn’s position until at least May 2016.

Most Labour MPs have not changed their opinion of their leader, continuing to regard him as irrevocably flawed. But neither have the members, who think the opposite. Indeed, support for Corbyn may now be higher than at the time of his election in September. More than 100,000 members have joined the party since then, while around 30,000 others have departed in protest, with the net result that Labour’s activist base has moved further leftwards. Under the party’s new electoral system, it is the grass roots that are sovereign.

Ever since Corbyn’s election, his opponents have discussed a possible means of bypassing the membership. Labour’s current rules do not explicitly state whether he would automatically be on the ballot if challenged. Were Corbyn required to reseek nominations from MPs, some suggest, he could be excluded from any contest. There is persistent speculation that the Labour leader’s office will act to clarify the matter. But most opponents now privately believe that activist pressure would ensure that Corbyn achieved 35 signatures if required.

In these circumstances, loose talk of a breakaway increases. But MPs’ tribal loyalty to the party, the first-past-the-post electoral system and the failure of the Social Democratic Party in the 1980s all mitigate against a split. Instead, the cold war between Corbyn and the parliamentary party will endure, with both sides locked in a permanent arms race.

In February, elections to Labour’s ruling National Executive Committee (NEC) will be studied closely. Corbyn’s ally Jon Lansman, a veteran of Tony Benn’s 1981 campaign for the deputy leadership and the editor of the Left Futures website, is reputed to carry a colour-coded chart assessing the leader’s strength among the 33 members of the NEC. Were Corbyn to be challenged directly, it is the NEC that would rule on the process for an election.

Mindful of his weakness among MPs, the leader and his supporters will seek to maximise his strength among members. Proposals to transfer greater policymaking powers to activists – Tony Benn’s old dream – will be tabled. Corbyn allies speak of using electronic ballots to canvass opinion on divisive issues such as the renewal of Trident. Outnumbered by multilateralists in his shadow cabinet, the leader will likely offer a free vote on the matter when the government tables a motion for renewal in 2016. Yet, as in the case of the vote on air strikes against Isis in Syria, the process by which that decision is reached will be fraught.

The sternest test of Corbyn’s electability to date will come in May when elections are held in Scotland, Wales, London and metropolitan boroughs in England. Should Labour be defeated in each, he could face a formal challenge. But if, as some expect, the party outperforms low expectations and Sadiq Khan becomes the first Labour mayor of London since 2008, Corbyn will certainly make it to Liverpool in September for his second conference as leader.

Whether before or after May, he will likely hold a shadow cabinet reshuffle to strengthen his position among the 31-member team (just three of whom voted for him). Clive Lewis, the energetic shadow energy minister and former army reservist, is among those tipped for inclusion. But the youth of Corbyn’s 14 supporters among the 232 Labour MPs, seven of whom were elected for the first time in 2015, restricts his room for manoeuvre, as does the age of others.

Surveying a party more profoundly divided than for thirty years, Frank Field, the Labour chair of the work and pensions committee, suggested the election of two leaders: one to represent MPs and one to represent members. Neither side will endorse the proposal but it exposes Labour’s fragmentation. Corbyn has both a stronger mandate among members and a weaker mandate among MPs than any of his predecessors. The question that both sides daily contemplate is whether anyone can command support among both.

Until Corbyn or an alternative is capable of doing so, Labour will remain united in name but divided in spirit.