So get back in your vehicle before you die.
He adds: "Put your hands on the auto and get ready to die, this is a citizen's arrest".
He called Mr Gale's wife a "big s**t", and not even their 11-year-old son was spared, Mr Beeley pointing at him and saying he too was a "w****r" and under arrest.
The passenger asks a passer-by to act as a witness, who then bravely tries to stand up to the BBC director.
During the heated exchange Mr Beeley told the family he was "trying to stop a death on the roads".
He then claims the woman punched him, which she instantly denies.
He alleged he had been "assaulted" by a family member and told the witness: "You didn't see what happened on the motorway with risky driving". He kept shouting he was going to make a citizen's arrest.
Gale, who was driving the family's second auto, claims he was grabbed round the throat by Beeley and he "raised his fist in a threatening manner".
Gale, of Salisbury, Wiltshire, said: "It was quite a scary thing".
Beeley flew into a "raving state" after his auto was forced to pull over at the side of the motorway. Beeley says. "In fact, I want you dead right now".
The UK is still the road rage capital of the world, with almost nine in ten UK drivers saying they had been road rage victims at least once, a new survey has found.
Police said in a statement: "We were called to a non-injury road traffic collision on the M27 between junctions 5 and 7 at 11.30am on July 22".
Police said the two men involved in the incident decided not to pursue a complaint.
"When officers attended all parties had moved to the Sainsbury's auto park in Hedge End".
When police arrived at the vehicle park near Southampton, nobody was taken into custody, but assault allegations by both men were recorded.
"As a result, advice was given to both parties and they were told that two assaults will be recorded and filed".
Beeley, from Badminton, studied anthropology at the University of Durham after spending his year overseas working with the Pitjantjatjarra tribe in Central Australia, his website states.