A new fly-on-the-wall documentary on Jeremy Corbyn's leadership gives a revealing insight into the mentality at the top of the Labour party.

Much of the programme is devoted to Corbyn and his closest advisers' complaints about left-leaning commentators and Labour MPs. The Guardian's Jonathan Freedland is described by Corbyn as "not a good guy," after writing an "utterly disgusting" piece criticising the Labour leader's attitude to antisemitism.  The New Statesman's George Eaton is described by Corbyn's policy chief as "the worst judge of anything". Eaton's crime it turns out, was writing a positive review on one of Corbyn's PMQs performances. The BBC, which for years has been accused by those on the right of being part of some grand left-wing conspiracy, is derided by Corbyn as "obsessed" with trying to destroy him. Even Corbyn's own team doesn't escape censure, after his communications chief Seumas Milne accuses one of them of secretly leaking their meetings to the Tories.

Meanwhile the actions and words of their real opponents in the Conservative party barely gets a mention. When Iain Duncan Smith resigns over Osborne's budget, Corbyn's team writes him a speech designed to exploit the division within the government. Yet for some reason Corbyn chooses to excise almost all of the attacks, explaining that "it's not up to me [to say] the government's a mess".

The question of whose responsibility it is to say the government's a mess, if not the leader of the opposition, is left hanging in the air. Presumably it's for those same commentators and journalists Corbyn believes are in a conspiracy against him.

The documentary was particularly revealing, coming as it does, the day after Labour's new London mayor Sadiq Khan was criticised by the shadow chancellor for appearing alongside David Cameron at an EU referendum event. When asked about Khan, McDonnell told an audience that sharing a platform with the Tories "discredits" Labour. He later denied that his comments were aimed at the London mayor. However, in a statement about the row issued afterwards, he added that "it doesn't help us appearing on platforms with Tories". Now leaving aside the hypocrisy of McDonnell's comments – he himself has repeatedly shared platforms with Tories on issues ranging from airport expansion to closing Guantanamo Bay – it is incredible that the shadow chancellor should choose Khan of all people to criticise at this moment.

Just a few weeks ago, Khan won the biggest election victory for the Labour party in over a decade. He did so on a broadly left-wing ticket which included commitments to cut travel and housing costs and tackle air pollution. And he did so in spite of a vicious Conservative campaign which sought to exploit racist fears about the election of London's first Muslim mayor.

If the Labour leadership had any sense they would be hugging Khan so close he could barely breathe, while praising him to the heavens as an example of the Labour party in action. Instead they have all but ignored his victory. Corbyn failed to appear at Khan's signing-in ceremony and did not even mention him at the first prime minister's questions following his victory, leaving it to the Liberal Democrat leader Tim Farron to congratulate him instead.

The two men are clearly no great fans of each other. Khan has repeatedly criticised his leader and was branded "hostile" in a leaked memo written by Corbyn's team. But the new London mayor is also in a unique position to sell Labour's message to the public. At a time when the Conservatives are trying to paint Labour as unelectable and unfit to govern, Khan is in the perfect position to show what Labour can do when given real power in the nation's capital.

More immediately, he's also in the perfect position to influence what now looks to be an incredibly close EU referendum campaign. A poll out yesterday revealed that almost half of Labour voters do not know where their party stands on the referendum. Whatever McDonnell may think of Khan's decision to 'share a platform' with the prime minister, Khan is clearly committed to trying to win the referendum. If McDonnell and Corbyn were similarly committed to getting their message out, then the race may not be as close as the polls currently suggest it is.

Watching the Vice documentary this morning I felt quite sorry for Corbyn's team, many of whom have clearly tried desperately hard to turn him into an effective opposition leader. This team, which initially included some serious operators, has gradually dwindled over the past year. In recent months three of Corbyn's most senior and respected members of staff – Simon Fletcher, Neale Coleman and Anneliese Midgley, have either been moved sideways or chosen to resign. None appeared in the Vice documentary.

Overall, the main sense I got from the documentary, presented by someone who voted for Corbyn in the first place, was the sense of a missed opportunity. The enthusiasm for Corbyn among his supporters and constituents featured in the programme was clear to see. The demand for a new kind of politics and a new kind of politician was obvious.

But after the best part of a year in the job, it's become increasingly clear that Corbyn and his closest advisers are more concerned with attacking those who might otherwise be sympathisers or allies, than taking on those who really do want to destroy his party. It didn't have to be like this. If Corbyn had instead sought to reach out to all wings of his party, while seeking out those in the media who might otherwise have given him a fair hearing, Labour might now be in a much stronger position. Instead the Labour leadership has become an increasingly insular operation, which seems more concerned with attacking its own side, than ever getting back into government again.

As long as that remains the case, Labour's future looks bleak.

Adam Bienkov is the deputy editor of Politics.co.uk

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