Sir Anthony Seldon warned Britain has not been so “polarised” since the Second World War and such deep division could lead to violence.
The historian told talkRADIO’s Alastair Stewart much of the division comes from a lack of clarity over who holds the final say on Brexit.
“What is the ultimate authority in Britain? Is it the courts, is it Parliament, is it the Prime Minister who says that he is acting out the will of the people as expressed in the referendum?” he said.
“It is unpredictable times at the moment and it will become dangerous if people start taking to the streets.”
Demonstrators for and against Brexit have held protests across the country since Boris Johnson announced plans to suspend Parliament for over a month.
A large crowd of anti-Brexit protesters gathered outside Parliament on Wednesday night, before marching towards Downing Street. More demonstrations are expected to be held across the weekend.
Sir Anthony said the situation is not yet dangerous, and compared to the rest of Europe Britain has been “quite a passive nation”, but this can quickly change.
“By and large we don’t do these kind of things in Britain but if one side or the other became so outraged then this would become a moment of danger,” he said.
“It would become dangerous if the government lost control of the people, I mean this is the moment when you move from a political crisis through a constitutional crisis to a national crisis.”
He added: “Just because Britain has been passive in the past doesn’t mean it has to be in the future.”