Tommy Robinson says he has gone abroad and is seeking to relocate because he believes his family are no longer safe in the UK.
A video circulating on social media shows Mr Robinson discussing an arson "incident" several weeks ago.
"It was targeted against my wife's property," he said. "At that point we left the country straight away and I'm looking at relocating my family, which is pretty hard to do, especially with Covid — I couldn't even get a hotel."
During the video Mr Robinson, whose real name is Stephen Yaxley-Lennon, refers to a recently imposed 14-day quarantine, leading to speculation he may be in Spain.
The former English Defence League leader said he drove to where he is staying now and he will not be returning to the UK for a planned demonstration this weekend, as he needs to remain with his family.
He said: "Obviously my wife has had enough of everything — someone gave her somewhere to stay, so we left the country, and I was due to be flying back for the demonstration, but now with this 14-day quarantine, I probably won't get back out and my kids are out here."
Mr Robinson said he has sorted new schools for his daughters, adding: "I'm still in the process of finding a permanent relocation for them."
He added: "I need my family to be away because they are not safe basically."
Mr Robinson claimed the alleged incident took place following his comments denouncing Black Lives Matter protests sparked by the death of George Floyd in the US.
Last month, Democratic Football Lads Alliance called on supporters to travel to London to protect monuments after some were vandalised during recent protests. Mr Robinson expressed his support for the action.
The video update from Mr Robinson has been shared hundreds of times on Twitter.
He was banned from Facebook and Instagram last year for violating their "community standards".
Watch the latest videos from Yahoo UK