The comedian and activist Eddie Izzard has marked his arrival on Labour’s ruling national executive committee by saying the “stain of antisemitism” present among “a minority” of members has to be removed.

He said Labour had to “make amends and repair the damage with the Jewish community”, in line with the commitment given by Jeremy Corbyn, the party leader, to tackle antisemitism.

Izzard was promoted to the NEC after the resignation of Christine Shawcroft on Saturday night. Shawcroft, a Corbyn ally, had been under pressure to quit since it emerged she had opposed the suspension of a Labour councillor accused of Holocaust denial. Izzard took her place as the runner-up in the NEC elections.

He spoke out as the party dismissed the implications of a Sunday Times investigation that found 12 officials working for Corbyn or John McDonnell, the shadow chancellor, were members of Facebook groups that routinely featured anti-Jewish, violent or abusive messages.

Izzard ran for election to the NEC with the support of Labour centrists, and the resignation of Shawcroft – which was initially resisted by the leadership – will marginally weaken Corbyn’s majority on the body that takes key decisions about party management.

However, Izzard stressed his support for Corbyn, saying: “We must unite our party around the platform of hope that Jeremy Corbyn has built so that we can kick out this terrible Tory government and build a Britain for the many, not the few.”

Commenting on the flurry of antisemitism allegations that have engulfed the party over the last week, triggered by the revelation that in 2012 Corbyn posted a message on Facebook backing the creator of an antisemitic mural, Izzard said he had campaigned against hate all his life.

“This is a very important time for the Labour party and we must stamp out completely the stain of antisemitism from a minority of members. It has no place in our party,” he said. “We must make amends and repair the damage with the Jewish community as Jeremy Corbyn has promised to do.”

The Sunday Times reported that a two-month investigation into 20 of the biggest pro-Corbyn Facebook groups – headed by We Support Jeremy Corbyn, which has 67,000 members – had uncovered more than 2,000 racist, antisemitic, misogynist, violent and abusive messages.

The paper said 12 Labour staffers working for Corbyn or McDonnell were members of these groups. But it did not provide evidence of any of them posting or supporting offensive messages, and a Labour source said the staff members identified by the paper were adamant they had not seen offensive material of the kind flagged up by the Sunday Times.

“This has been written up in a way that makes it look as if these people were active and complicit in the abuse,” said a senior party source. “But a lot of these people did not even realise they were members of these groups. On Facebook you can be added to a group without your knowledge. That happens quite often.

“And there is nothing wrong with being a member of a Facebook group that supports the Labour party. Most of the messages in groups like this are about what a particular CLP [constituency Labour party] is doing, or about the anniversary of the NHS.

“Being a member of a group is not evidence of having regularly checked the group and trawled through the comments, and our staffers are crystal clear about not having seen this abusive material.”

Labour has a specific social media policy that says abusing someone online is “just as serious as doing so face to face” and that the party will take action against it.

A party spokesman said: “These groups are not run by the Labour party or officially connected to the party in any way. The Labour party is committed to challenging and campaigning against antisemitism in all its forms.”