The former Labour leader Neil Kinnock has stepped up his criticism of Jeremy Corbyn, denouncing him as “vain” and urging people to join the party so they can vote him out of office.

In an interview with the Guardian, Lord Kinnock also criticised Corbyn for not campaigning hard enough to keep Britain in the EU. He insisted that if the Labour leader does face a leadership challenge, he would need the support of 50 MPs or MEPs to get on the ballot paper – a point contested by Corbyn’s allies.

Angela Eagle, the former shadow business secretary, on Friday reiterated her determination to stand against Corbyn for the leadership if he does not resign. She has held off until now to see if talks convened by the Unite general secretary, Len McCluskey, can broker a compromise, but so far no deal has emerged and one anti-Corbyn MP said colleagues were losing patience with McCluskey’s efforts.

Until recently Kinnock had been relatively restrained in his public criticism of Corbyn, but at a private meeting of the parliamentary Labour party he received a standing ovation after delivering a speech saying Corbyn should stand down. In his Guardian interview he said he was “bloody angry” about politics generally, but particularly about Labour. “People divide into those who are vain and those who are not. And Jeremy is a vain man,” said Kinnock, referring to Corbyn’s refusal to resign after losing a no-confidence motion among Labour MPs.

Kinnock, who is now a peer, said a party that went into an election with a leader who did not command the confidence of MPs was “not taking itself or its mission seriously” and he urged people to join the party now to take part in the leadership election that seemed imminent.

He said: “Labour supporters across Britain recognise that the 172-40 vote of no confidence in Jeremy Corbyn came from MPs who are constantly in touch with voters and dedicated to trying to make Labour electable. They have made it clear that he cannot give the leadership that is vital to gain credibility and national appeal for our party.”

Kinnock said Corbyn’s performance during the referendum campaign showed that “either he, or people influencing him, really didn’t want to put too much effort in” to keep Britain in the EU and he insisted that, if Corbyn is challenged, he would need the support of 20% of MPs and MEPs to be a candidate. That was the rule when he was the Labour leader in 1988 and was challenged by Tony Benn, he said.

The issue is important because the current rules are ambiguous on this point and because Corbyn would struggle to get the 50 nominations if he had to. Labour’s general secretary, Iain McNicol, has reportedly had legal advice saying Corbyn would need 50 signatures, but Corbyn’s allies have legal advice saying the opposite and the issue would have to be resolved by the national executive committee, which is split fairly evenly between Corbyn’s supporters and opponents.

In his interview Kinnock also spoke about the PLP meeting where he delivered his speech, which was secretly recorded and posted on the internet on Friday. “Even people who had not voted for the no-confidence motion [last week] got up and said, ‘I’m now part of the 172 [who voted for it]’. One of the women MPs said, ‘It’s now 173’. Then one of the men called across, ‘No, it’s 174’,” he said.

Kinnock said he had not intended to speak, but that he was provoked by Corbyn supporter Dennis Skinner who accused MPs of thinking they were more important than members. Kinnock responded with a speech recalling the creation of the party, saying the leader had to have the confidence of MPs because Labour was established to pursue a parliamentary route to socialism.