Jeremy Corbyn has argued that the BBC is obsessed with trying to damage his leadership and accused some within Labour of playing into its hands.

The party leader made the claim in an interview with Vice News as part of a fly-on-the-wall documentary that gives an insight into the workings of his office.

The film, published on Wednesday morning, follows Corbyn over almost two months leading up to the May polls – through the party’s response to the unravelling of the budget, the launch of its inquiry into antisemitism within the party, and the election campaign.

In a series of interviews with Ben Ferguson, a Vice journalist and Labour member who voted for him as party leader, Corbyn revealed the depth of his feelings about his portrayal in the media.

In response to Ferguson expressing concern about Labour’s performance in May, Corbyn said: “There is not one story on any election anywhere in the UK that the BBC will not spin into a problem for me. It is obsessive beyond belief. They are obsessed with trying to damage the leadership of the Labour party and unfortunately there are people in the Labour party that play into that.”

Corbyn also said one of the main things he had learned as leader is “how shallow, facile and ill-informed many of the supposed well-informed major commentators are in our media”, accusing them of shaping a debate that was “baseless and narrow”.

The Labour leader is filmed complaining on the phone about a Guardian column expressing the view that Labour under Corbyn and the wider left have a problem with antisemitism. Corbyn, who was speaking to his director of strategy, Seumas Milne, called the column “utterly disgusting”.

The film shows the discussions around Corbyn’s speech in parliament after Iain Duncan Smith resigned as work and pensions secretary. Afterwards, the Corbyn was criticised for not sufficiently exploiting Tory divisions.

Milne is seen writing a draft of the speech before Corbyn changes it to cut down criticism of government turmoil over the budget and welfare. The Labour leader then says: “It’s not up to me to throw in other than a couple of lines about the government’s in a mess.”

Corbyn during the local election campaign. Photograph: Joe Giddens/PA

The film shows some of his staff believe his questions to the prime minister are often leaked from his office.

In a sign of tensions within his inner circle, Milne told Vice News that the questions appear to have been leaked on about one in three occasions, giving the prime minister an advantage.

The Vice journalists had unprecedented access to Corbyn and his close associates, including a brief interview with the leader’s wife, Laura Alvarez. She praised her husband’s response to David Cameron’s PMQs jibe about his mother thinking the Labour leader should put on a tie and sing the national anthem. “Jeremy stood very strong. It was amazing,” she said.

The film shows Corbyn signing photographs, tiles and books for supporters, and promising to autograph apples from his allotment in the autumn.

It also allows a glimpse into his PMQs preparations, where staff take on the role of Cameron. It shows Corbyn joking “Does anyone want to be prime minister?” before Andrew Fisher, who was recently promoted to be his policy chief, steps up.

In terms of divisions within Labour, Corbyn argued the atmosphere in the parliamentary party had completely changed since the leadership election, when most MPs did not support his campaign. But he acknowledged there are “some who are harder fish to catch”.