Jeremy Corbyn is discovering the art of messy compromises that sometimes please no one. A year ago, his power to decide Labour’s strategy was unchallenged. His allies kept the tricky Brexit issue off the Labour conference agenda. Even Corbynsceptic MPs acknowledged he had earned their support by depriving the Conservatives of their Commons majority.

The mood at this year’s Liverpool conference is very different. Corbyn’s supporters retain their enthusiasm for the Labour leader and, with the Tories making such a mess of Brexit, hope it might just result in a general election. But, after 12 months in which the antisemitism row and foreign policy have loomed large, Corbyn’s MP critics are once again detached, and agonising over whether to leave their party. Some haven’t bothered to attend the conference, while others are making only a fleeting visit.

Against his wishes, Corbyn has been forced to take a small but significant step towards backing a Final Say referendum on Brexit. After five hours of wrangling last night, Labour cobbled together a motion to be debated tomorrow which moves the party on from keeping all options on the table if it cannot get an election, by adding the words “including campaigning for a public vote”.

Last night’s meeting rejected calls by Corbyn allies to restrict a referendum to “the terms of Brexit,” which would have stopped Labour offering voters a chance to remain in the EU. That decision cheered supporters of a Final Say vote. They went to bed happy last night. But they woke up to a conference headache, and not for the usual reason: they were alarmed to hear John McDonnell tell the BBC’s Today programme that Remain would not be on the referendum ballot paper. “That is not Labour’s policy,” one referendum campaigner told me. “The leadership lost that battle last night.”

But Labour has moved. There is something for Final Say supporters to welcome, even though their battle is not won yet. Corbyn allies believe nothing has really changed because his hands are not tied.

Another contrast with a year ago is that Corbyn’s cheerleaders are fighting among themselves. The new divide is between the grassroots Momentum group and the trade unions. Left-wing activists are bitter that the unions watered down Momentum’s proposal for MPs to face “open selection” between elections, a cuddlier form of words for mandatory reselection. A milder rule change was approved by the conference, under which MPs will face a selection contest open to other candidates if a third of a constituency party’s member or union branches demand one, a lower threshold than the current 50 per cent. Momentum is disappointed that Corbyn’s internal democracy review produced only “a meagre set of reforms” and vowed to fight on for “open selection”.

Labour Party conference 2018: in pictures Show all 24 1 /24 Labour Party conference 2018: in pictures Labour Party conference 2018: in pictures Leader Jeremy Corbyn addresses a pre-conference rally at Pier Head in Liverpool on Saturday Getty Labour Party conference 2018: in pictures Deputy leader Tom Watson cycles at the party conference as part of the Labour Cycles scheme PA Labour Party conference 2018: in pictures Leader Jeremy Corbyn and Deputy Leader Tom Watson sit together on stage on Sunday Reuters Labour Party conference 2018: in pictures Shadow Chancellor John McDonnell speaks at a fringe event at the party conference on Sunday REUTERS Labour Party conference 2018: in pictures Delegates are welcomed to the conference at the Arena and Convention Centre in Liverpool Getty Labour Party conference 2018: in pictures Shadow Chancellor John McDonnell speaks at a fringe event at the party conference Reuters Labour Party conference 2018: in pictures Leader Jeremy Corbyn and Shadow Foreign Secretary Emily Thornberry attend a vigil in Liverpool for those who are affected by the war in Yemen PA Labour Party conference 2018: in pictures Anti-Brexit supporters demonstrate outside the conference in Liverpool on Sunday Getty Labour Party conference 2018: in pictures Anti-Brexit supporters demonstrate outside the conference in Liverpool on Sunday PA Labour Party conference 2018: in pictures Mayor of London Sadiq Khan arrive at the conference on Sunday EPA Labour Party conference 2018: in pictures Shadow Chancellor John McDonnell speaks at a fringe event at the party conference EPA Labour Party conference 2018: in pictures Delegates at the Arena and Convention Centre in Liverpool, where the conference is being held PA Labour Party conference 2018: in pictures Badges worn by a delegate at the conference on Sunday EPA Labour Party conference 2018: in pictures Shadow Home Secretary Diane Abbott speaks at a fringe event at the party conference EPA Labour Party conference 2018: in pictures Anti-Brexit supporters demonstrate outside the conference in Liverpool on Sunday Reuters Labour Party conference 2018: in pictures Deputy leader Tom Watson poses for a selfie on Sunday AFP/Getty Labour Party conference 2018: in pictures Leader Jeremy Corbyn listens to a speech on Sunday Getty Labour Party conference 2018: in pictures General Secretary of the Labour Party is welcomed to the stage by leader Jeremy Corbyn on Sunday Reuters Labour Party conference 2018: in pictures An anti-Brexit protester Reuters Labour Party conference 2018: in pictures Leader Jeremy Corbyn speaks at a vigil in Liverpool for those who are affected by the war in Yemen PA Labour Party conference 2018: in pictures An anti-Brexit protester AFP/Getty Labour Party conference 2018: in pictures Anti-Brexit supporters demonstrate outside the conference in Liverpool on Sunday AFP/Getty Labour Party conference 2018: in pictures Leader Jeremy Corbyn and Deputy Leader Tom Watson sit together on stage on Sunday Reuters Labour Party conference 2018: in pictures Anti-Brexit supporters demonstrate outside the conference in Liverpool on Sunday Reuters

If Corbyn hoped that Momentum’s failure to win it would allay MPs’ fears about being deselected, he will be disappointed. “We know the left are coming for several of us; the rule change will make it easier,” groaned one MP. There’s talk of Corbynsceptics resigning the Labour whip in small groups, rather than going solo like Frank Field. Another MP admitted: “Having spent a lifetime trying to get a Labour government into power, I’m now in the incredible position of doing everything I can to stop Corbyn becoming our next prime minister. It’s heartbreaking.”

Of course, Corbyn loyalists might argue the party would be better off without such dissenters. But they are nervous, knowing that a new centre party could divide the anti-Tory vote, as the breakaway SDP did at the 1983 and 1987 elections.

I am told that Tony Blair wants to lead a new centre party, despite his apparent denials. But even his admirers are divided over whether he should. Some ask: what would be the point of what would inevitably be dubbed a “Blairite” party without the man himself? If he were guiding another leader from the wings, why not lead it himself?

Lacking another obvious leader, Blair would be such a party’s greatest asset but also its biggest weakness, since he is toxic for many voters and his involvement would only remind everyone of the Iraq War (which would suit Corbyn, whose hands are clean).