Clause One of the Labour Party's constitution commits it to maintaining a strong parliamentary party:
“[The party’s] purpose is to organise and maintain in Parliament and in the country a political Labour Party.”
Given that Jeremy Corbyn is opposed by 95% of his own MPs (only 15 MPs voted for him in the 2015 ballot; he wasn't required, as the incumbent leader, to check out that support again in 2016), the first obvious division within Labour would appear to be that between those who want to maintain a strong parliamentary party (the MPs who opoosed Corbyn) and those who want to make it more a grassroots-run organisation (principally Corbyn supporting groups like Momentum and the Campaign for Labour Party Democracy). This New Statesman editorial summarises and comments on the division.
The policy differences, of course, are severe. The leaking of Labour's election manifesto suggested serious opposition within the party to it. It has become a fundamentally binary struggle between one-time Blairite or "centrist" Labour members (the majority of the parliamentary party) and the more left-wing, nationalising tendency (Corbyn and his grassroots supporters).
The "Economist" neatly summed it up thus:
Labour is not so much an organised political party as a blood-soaked battleground between two warring factions: the far-left faction, led by Jeremy Corbyn and John McDonnell, and including acolytes such as Dianne Abbot and Emily Thornberry, and “moderate” Labour. “Moderate” Labour consists of the bulk of their MPs, including Yvette Cooper, the moderate wing’s current leader and wife of Gordon Brown’s right-hand man, Ed Balls, Stephen Kinnock, the son of the party’s former leader, Neil Kinnock and Hillary Benn, the son of the left’s former champion, Tony Benn, as well as the majority of traditional Labour voters. The Corbynistas consist of hard-left activists, many of them former members of Marxist groupuscles, who joined the party in huge numbers in the past couple of years. The manifesto is pure Corbynism. The leak is clearly an attempt by the anti-Corbyn faction to embarrass Mr Corbyn and derail his launch.
(The whole piece - from Bagehot - is worth reading).
The moderate Labour faction draws its ideological position from the recent history of New Labour, personified by Tony Blair and given shape by Peter Mandelson (and, as it happens, Gordon Brown despite his attempts to subvert it through personal opposition to Blair). More distantly, it is comparable to most previous Labour leaders such as Wilson and Gaitskell, fundamentally social democrats who believed in working effectively through parliament to gradually change Britain's economic and social institutions towards achievement of the cause of equality. They propounded a broadly "strong", pro-US foreign policy (supporting British possession of a nuclear deterrent) with the belief in a mixed economy. Blair's spin on this was outlined in the so-called "Third Way", a belief that Labour's brand of social democracy had to adapt to the post-Thatcher era by embracing privatisation but coupling it to the public sector (Public Private Partnerships). He also adopted a more clearly socially liberal attitude (notably in the field of liberalising legislation on same-sex relationships).
The left-wing Labour faction of Corbyn has a new movement supporting it (Momentum) and an old one (the Campaign for Labour Party Democracy). Somewhat ironically the CLPD is an old Bennite movement. Tony Benn was the leader of the left in the 1980s, the last time Labour took a severe leftward turn, and his son Hillary is now one of the leading moderates in the parliamentary Labour Party, sacked as shadow Foreign Secretary by Jeremy Corbyn. This left grouping draws its ideological position from a more radical, even revolutionary brand of socialism that despises the democratic socialism of the moderates. They believe in a grassroots movement and a return to a state run economy, coupled with more recent cultural issues related to diversity and opposition to "country" actions like hunting and badger culling. They also tend to embrace immigration as a positive force.
The divisions above seem straightforward enough - a classic left v right - but are muddied by the division of ordinary Labour supporters into social activists and traditional members. The social activists who dominate Momentum are young, active on social media and committed to a range of left social causes. The traditional Labour members are more conservative socially, oppose immigration and also tend to favour Brexit (which Corbyn, after much hesitation, supported and continues to support). For Labour's electoral success, much depends on where these traditional members and voters decide to cast their vote, with early polling evidence suggesting that many would not vote for Corbyn.
The moderate, or social democratic, element of the Labour Party remain in a quandary. The Labour leadership has moved far away from them, taking with it many of their constituency memberships. There is no guarantee that Corbyn would leave the leadership if he loses (he has said that he will stay on) and should the October conference approve a further reduction in MPs' power to select future leadership candidates, they may find it impossible to restore a moderate leadership. Which begs the question of where they go. They are ideologically opposed to the Liberal Democrats, but the last example of moderate Labour MPs trying to form a new parliamentary grouping and national party - the Social Democratic Party of the 1980s - was ultimately a failure.
If Corbyn wins - an unlikely scenario even given the Yougov poll projecting Tory seat losses - then moderate Labour MPs will find themselves having to support a left-wing Labour government whose policies they fundamentally disagree with, or opposing their own party in government and signing their death warrant in the constituencies.
Win or lose, Labour's existential crisis isn't going away.