The original track, which the band sang with Kirstie MacColl, contains a homophobic slur which the BBC opted to replace.
The slur “f****t” has been exchanged for “haggard”, while the term “s*ut” has been muted all-together when played on BBC radio stations.
Fox tweeted an announcement of the BBC’s decision and wrote: “Here we go again.
“The cultural commissars at the @bbc are telling you what is and isn’t appropriate for your ignorant little ears. Wouldn’t it be nice if we sent the (proper) version to the top of the charts? #DefundTheBBC. RT.”
The Pogues retweeted Laurence and wrote: “F**k off you little herrenvolk s***e.”
The term “herrenvolk” means “a race, nation, or group, such as the Germans or Nazis as viewed by Hitler, believed to be superior to other races.”
Fox is yet to respond to The Pogues.
In September, Fox announced that he was launching his own political party, the Reclaim party, which has been dubbed the “Ukip for culture.”
The actor claims he wants to celebrate British history, defend freedom of speech, and reform public institutions such as the BBC.
In a statement earlier today, the BBC said: “We know the song is considered a Christmas classic and we will continue to play it this year, with our radio stations choosing the version of the song most relevant for their audience.”
Fox made headlines earlier this year during a January Question Time appearance, in which he accused an audience member of racism after she branded him a “privileged white male.”
He had appeared on the show and disputed claims that the coverage of Meghan Markle in the press had been racist.
There followed a social media storm, followed by further comments from Laurence on topics such as the inclusion of a Sikh soldier in World War One flick, 1917.
His Twitter feed has since sought to grapple with “woke” culture.