MPs have written to Facebook and Twitter demanding they take down an “abhorrent” video supporting and promoting the banned far-right organisation National Action.

Yvette Cooper, writing on behalf of the home affairs select committee, told the social media giants it was “completely unacceptable” that the video was still available on both platforms despite being taken down by YouTube.

National Action, whose members praised the murder of Labour MP Jo Cox in 2016, was proscribed as a terrorist organisation by the government in December 2016. They have been found to be “incredibly active and still very much involved in extremist politics in this country” by the anti-fascism organisation Hope Not Hate.

Mark Rowley, a former head of counter-terrorism for the Metropolitan police, said the public should be “gravely concerned” about the group.

Last week a British army veteran who served in Afghanistan and was described as an “outstanding” soldier was among a group convicted of being members.

National Action was connected to a plot to kill the Labour MP Rosie Cooper. The plot was uncovered when a disillusioned member tipped off the campaign group Hope Not Hate.

In letters dated 19 November, Cooper wrote: “National Action praised the man who murdered a member of parliament in June 2016, and supported a recent plot to attack another. We are therefore extremely concerned that such abhorrent views are still being given a platform on Facebook/Twitter – especially when it is the same video that YouTube have already accepted is illegal and have taken down.”

“Your platform is one of the most prominent in the world; you have access to some of the most advanced technologies which you use extensively to prevent breaches of copyright; and you employ some of the best technological minds. We do not understand why you have not prevented the upload and spread of the same illegal material after it has been so publicly raised with your colleagues at Google/YouTube.”

Cooper has demanded that Twitter and Facebook explain by 3 December:

• How and why a known video from a banned terrorist organisation was allowed to be uploaded to, and remain publicly accessible on, their platforms for so many months, and whether it is possible that it is still available.

• What steps were taken to tackle National Action content following the committee’s raising of this issue with Google/YouTube earlier this year.

• Whether, and how, they share information on known illegal content with their colleagues at other technological and social media companies.

• What training their content reviewers and moderators receive on identifying content relating to banned UK terrorist organisations and on far-right material.

• An update on how many trained content moderators they employ directly and how many are employed through outsourced companies, and how many of these are based in the UK.