“I sincerely apologise to the owners of the mare, the staff who cared for her, the horseracing industry and all followers of horse racing for my actions.
“To try defending my stupidity at the time would add further insult and hurt to the many loyal people that have supported me during my career. I have caused embarrassment to my employers, my family and most importantly the sport I love.
“I am heartbroken by the damage I have caused and will do my best to try and make amends to those hurt by my conduct.”
The video has surfaced just 24 hours after Elliott hit the headlines for a horrific photo of himself saddling a dead horse.
The 43-year-old has trained greats such as two-time Grand National winner Tiger Roll and unbeaten Envoi Allen.
The BHA said in a statement: “The action taken by the BHA recognises that Mr Elliott is licensed in Ireland, whose regulatory body is carrying out its own investigation. However, Mr Elliott has entered horses to race in Britain, from which point the British Rules of Racing apply to him.