Andrew Neil, the veteran political broadcaster, has attacked the BBC for promoting “anti-British drivel” on its children’s website to mark the day Britain left the EU.

Neil, whose Andrew Neil Show is aired on BBC Two and who is also a presenter on Politics Live, took to Twitter to complain about a sketch song featured in an archive selection of Horrible Histories favourites put together on CBBC iPlayer and also made available on YouTube to mark Britain’s departure.

The offending song, British Things, a popular comic number from 2009 starring Mathew Baynton as a footman and Sarah Hadland as Queen Victoria, shows the monarch being taught where all her “British things” really come from, including tea, sugar and cotton.

Neil commented: “This is anti-British drivel of a high order. Was any of the licence fee used to produce something purely designed to demean us?”

The satirist Nish Kumar, host of The Mash Report on BBC Two and one of the new hosts of BBC Radio 4’s News Quiz, hosted a selection of Horrible Histories sketches chosen because they featured references to French, Italian and German history.

One song made fun of the Italian interest in clothes, while another showed Norman soldiers dancing together in a parody of the Gangnam Style club hit of 2012.

Neil’s criticism of the BBC for promoting this content was later picked up by Piers Morgan, who said: “Why is the BBC paying nasty pieces of work like Kumar to trash Britain like this? An outrageous, shameful abuse of public money.”

Kumar, who has previously been attacked by Neil as part of “unfunny” politically-correct BBC satirical output, introduces the Queen Victoria song with a quip about Britain deciding to go it alone after a long and bumpy ride to Brexit. The footage was chosen to promote the online feature. In the song’s most pointed lyric, Baynton’s footman emphasises that these “British” goods have come to the Queen’s palace via slave labour.

The comedian Emma Kennedy stepped up to defend the song on Twitter, asking: “Drivel? Which bit of it is factually inaccurate?”.

Neil replied that he regarded the suggestion that people think tea and sugar are British was a false premise: “That anybody has ever claimed tea or sugar cane came from Britain. Doh.”

The squabble exposes heightened tensions about the tone set by the BBC at a time of political division and follows a week in which the corporation’s future funding via the licence fee has been questioned. The Tory MP Julian Knight was elected as the new chair of parliament’s culture committee and confirmed his intention to examine continuing to pay for the BBC in this way.

A BBC spokesperson said: “The Horrible Histories video is light-hearted and not anti-British. We are a nation, like most others, that enjoys a patchwork of traditions and culture from other countries. Our children’s audience are able to take these things as intended.”

Cuts to BBC news services were announced on Wednesday. The Match of the Day presenter Gary Lineker, one of the BBC’s most highly paid stars, also suggested last week that the licence fee should become a voluntary payment.

On Monday, he told the Guardian: “The licence fee is our fundamental problem. You’re forced to pay it if you want a TV, and therefore it’s a tax. The public pay our salaries, so everyone is a target. I would make the licence fee voluntary. I’ve always said for a long time, I would make it voluntary. I don’t know the logistics of how it would work. You would lose some people but, at the same time, you’d up the price a bit. It’s the price of a cup of coffee a week at the moment. If you put it up, you could help older people, or those that can’t afford it.”