Andrew Neil criticised the corporation over a video posted on the CBBC Twitter feed. The two minute clip was from satirical children’s show Horrible Histories.
It was presented by comedian Nish Kumar who introduced the video with a reference to Britain’s EU departure.
The video features Queen Victoria being shocked to discover goods she enjoys, such as tea and sugar, are not actually produced in Britain.
Mr 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?”
Critics pointed out it’s unlikely Queen Victoria would have thought either tea or sugar come from the UK.
Sugar was grown in the Caribbean whilst tea originated in China, but was later produced on mass in India.
The video clip has been viewed around a million times, partly because of the controversy it attracted.
In the introduction Mr Kumar comments: “Britain is striking out on its own and leaving Europe.”
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In response to the video Mr Martin tweeted: “Is the BBC on a mission to get itself closed down?”
However other social media users came to the BBC’s defence.
Writer Ian Fraser responded to Mr Neil by commenting: “Is there anything factually incorrect about this?
“Also isn’t it healthy that, just occasionally, British schoolchildren are made aware that not everything about Britain’s past is glorious?”
Mr Neil hosts The Andrew Neil Show on BBC Two and is also a presenter on Politics Live.
Britain officially left the EU at 11pm on Friday.
Thousands gathered in Parliament Square to celebrate the departure.
They celebrated Brexit by waving union jack flags and singing patriotic songs.
Boris Johnson released a video to mark the occasion.
He commented: “The most important thing to say tonight is that this is not an end but a beginning.”