The court heard a crew member was on the boat while it was heard leaking air.
Prosecutor Kevin Lucie, outlining the facts of the criminal damage charge, told the court that Thomas slashed an adrift boat with a knife and said: “You are on English territory. This is England. This is not France any more.”
Deputy Chief Magistrate Tan Ikram said the case could have been heard in the magistrates’ court but Mr Thomas elected to be tried at crown court.
Far-right activist Stephen Yaxley-Lennon, also known as Tommy Robinson, was among those in the public gallery.
Some supporters also gathered outside the court.
Posting on social media after the hearing, Yaxley-Lennon said: “Danny is being remanded to prison. Bail refused. Outrageous.
“His legal team will now prepare to fight at the crown court for his bail.”