Downing Street has said Jimmy Carr’s joke about the Holocaust was “deeply disturbing” but it is a matter for Netflix whether the comedian’s show should remain on its streaming service.

Carr known for his stand-up and hosting roles on shows like 8 Out Of 10 Cats, prompted criticism after a clip from his recent one-hour Netflix special, His Dark Material, was shared widely on social media.

In it, the comedian jokes about the horror of the Holocaust and “six million Jewish lives being lost” before making a disparaging remark about the deaths of thousands of Gypsies at the hands of the Nazis as part of the punchline.

The Prime Minister’s official spokesman said: “Those comments are deeply disturbing and it’s unacceptable to make light of genocide.”

The Government is “toughening measures for social media and streaming platforms who don’t tackle harmful content”.

Asked whether Netflix should pull the show, the spokesman said: “That will be a matter for them. We are clear that mocking the atrocities of the Holocaust is unacceptable.”

The Government was focused on “making sure that streaming services are more accountable”, he added.

Culture Secretary Nadine Dorries previously suggested new laws via the Media Bill could hold to account streaming sites for airing jokes such as those made by Carr.

Anti-hate groups such as the not-for-profit organisation Holocaust Memorial Day Trust and The Auschwitz Memorial have condemned the comedian for the joke.

The Traveller Movement, a charity supporting the traveller community in the UK, has also launched a petition calling for Netflix to remove the segment of the programme “which celebrates the Romani genocide”.

It said the joke in question was “truly disturbing and goes way beyond humour”.

On Monday morning, Health Secretary Sajid Javid told Times Radio the joke was “horrid”.

He added: “I think we all have a right to react to that, and one of the best ways anyone can react to that is show these platforms what they think about Jimmy Carr by not watching or listening to him, and that will send him a very strong message.”

Martin Docherty-Hughes, SNP MP for West Dunbartonshire, said he was “utterly dumbfounded” by Carr using the Holocaust to “poke fun at one of the most marginalised groups in these islands, the Roma and Gypsy community”.

He suggested the House of Commons should have an opportunity to hold a debate to recognise the “value and worth” of the Gypsy, Roma and Traveller community across the UK and to “raise them up, not to put them down”.

Carr issued a “trigger warning” to the audience at the beginning of his Netflix special and told viewers it contained “terrible things”.

According to The Mirror, he appeared to address the controversy during a performance at the Whitley Bay Playhouse on Saturday night.

Discussing so-called cancel culture, he told the audience: “The joke that ends my career is already out there.”

Netflix declined to comment.