Allen has been reported to call for the anti-Brexit campaigner and lawyer Gina Miller to be beheaded. He also called Miller "cow traitor" in the Facebook post.
In 2016, Miller launched a successful campaign to block the government from implementing Brexit without parliament's ultimate approval.
READ MORE: UK Gov't 'Could Be Guilty of Biggest Cover-Up in Decades': Gina Miller on Brexit
The man in question, Allen, also allegedly suggested a "full pig" should have been thrown at a mosque in Blackpool, England.
On a different occasion, he was reported to say to a woman before the 2016 vote on Britain's EU membership to "do yourself a big favour and vote out so you don't get raped of (sic) a migrant."
When he reportedly made the comments on social media three years ago, Allen was not yet a member of the UKIP, the party's chief Gerard Batten argued, adding he added his membership in April 2018.
"I deplore the remarks made and these in no way represent the views of me, UKIP, or the overwhelming numbers of our membership," Batten, who has been leader of UKIP since 2018, commented.
UKIP leader reportedly added that the BBC, who reported the development, would not taint the party's reputation by means of "guilt by association".