He seized the opportunity to give Mr Johnson his opinion by leaning out of his cab window and gesticulating vigorously with his hand, while simultaneously shouting: 'You're one of them, mate.'
A video filmed by a passerby reveals the foul-mouthed response from Mr Johnson, who is tipped as a future leader of the Conservative Party.
Wearing a yellow cycling helmet with his trademark blonde mop poking out the sides, Mr Johnson swore at the startled taxi driver.
The cabbie, continuing his vulgar hand gesture, repeats: 'That's what you are: one of them.'
Mr Johnson felt 'obliged' to reply with some 'choice words of his own', his friends claim.
The video shows him telling the cabbie again: 'Why don't you f*** off and die - and not in that order.'
At this point, their paths diverged, the cabbie driving on, muttering loudly out of his window: 'Yeah, b******s ... hope you die,' and Mr Johnson - a half-smile on his face - turning right towards his house. The altercation happened at 12.20am on Friday, June 5.
Last night a source close to the mayor said: 'I believe this particular cabbie is a serial heckler. He offered Boris a few choice words. Boris felt obliged to offer him a few in return. And off they went.'
Licensed Taxi Drivers Association spokesman Steve McNamara said: 'The taxi drivers in London are rightly worried about the way that private firms are operating.
'I can understand why the driver had a pop at Boris, and to be fair to him, he gave back as good as he got.'
The onlooker who filmed the row on his iPhone said: 'I didn't expect Boris to use such select words - maybe if he is going to be the next Prime Minister he should calm things down a bit.'
Tensions between Mr Johnson and London cabbies came to a head last month.
Mr Johnson was accused of 'not having the guts' to stand up to Uber, which is blamed for putting hundreds of black cabbies out of work in recent months.
He angered cabbies by suggesting they needed to accept they were being challenged by the powerful forces of the 'free market' and 'consumer choice'.
- Daily Mail