Nadine Dorries has suggested new laws would hold to account streaming sites from airing jokes such as those made by Jimmy Carr about the Traveller community and the Holocaust.

During an interview on Saturday’s BBC Breakfast, the Culture Secretary condemned the comic’s joke made during his one-hour Netflix special, His Dark Material, as “shocking, abhorrent and unacceptable.”

Carr issued a “trigger warning” to the audience at the beginning of the Netflix show, admitting his performance contained “terrible things”.

In a widely-shared clip from the show, the comedian joked about the horror of the Holocaust and “six million Jewish lives being lost” before making a disparaging remark about the deaths of thousands of Travellers at the hands of the Nazis as a punchline.

Dorries suggested that in the future, new laws would “hold Netflix to account” for such content.

“We are looking at legislation via the Media Bill which would bring into scope those comments from other video on-demand streaming outlets like Netflix,” she said.

“So it’s interesting that we’re already looking at future legislation to bring into scope those sort of comments.”

The MP said Carr’s comments were “abhorrent and they just shouldn’t be on television”, but it was then put to her that in a tweet in 2017 she had claimed that “left-wing snowflakes are killing comedy”.

She said: “Well, that’s not comedy.

“What Jimmy Carr did last night is not comedy. And you know, I’m no angel on Twitter, nobody is, but I just would like to say that nothing I’ve ever put on Twitter has been harmful or abusive.

“But that last night… Jimmy Carr’s comments, no one can call that, you know, snowflake or wokeishness, that’s just… it was just appalling.”

She said the comments were “shocking and abhorrent and unacceptable, not just because he was making fun on the basis of people who died in the most appalling circumstances, but on the pain and suffering of many thousands of families”.

In a separate interview with Times Radio, she said: “We don’t have the ability now, legally, to hold Netflix to account for streaming that but very shortly we will.”

Asked on Sky News if there was any way this new law would put restrictions on free speech, she said: “No, absolutely not. We’ve been very, very… well because I’m a Conservative, I’ve been very, very careful about that.”

In a tweet, Nadia Whittome, Labour MP for Nottingham East, has also urged Netflix to remove Carr’s “vile anti-GRT and antisemitic material”.

The Traveller Movement, a charity supporting the traveller community in the UK, said: “This is truly disturbing and goes way beyond humour.”

In a tweet, the charity said: “We need all your support in calling this out #StopTravellerHate @StopFundingHate.”

The charity has launched a petition to Netflix calling for the “removal of the segments of His Dark Material which celebrates the Romani genocide”.