The Conservative Party chairman James Cleverly has been accused of speeding and using his phone while driving following a collision with another motorist on the M11.
Mr Khan filmed his tense roadside exchange with Mr Cleverly, before revealing his claims in a series of tweets.
“This guy James Cleverly ... hit my car on M11 while speeding and using his phone.
“At the scene he admitted it was his fault. He damaged my new car. When I contacted him he said he is not accepting liability.”
The short video showed one of the two parked vehicles with a scratch and dent above one of the wheels, as the pair prepared to swap details for insurance purposes.
A spokesman for Mr Cleverly said he had been involved in a “minor accident” and the matter was now “being dealt with by his insurance company”.
Mr Khan also posted what he claimed to be a series of texts he exchanged with Mr Cleverly in which the Braintree MP appeared to reject any acceptance of fault or liability.
“It was your fault mate,” wrote Mr Khan. “I am trying to be nice ... but you are now pushing it mate.”
Sources close to Mr Cleverly denied that he was speeding, talking on his phone, or that he initially accepted liability for the collision.
It comes as MPs call for a ban on drivers using mobile phones in hand-free mode.
Earlier this month the Commons Transport Select Committee said current laws which only proscribe the use of phones being held by drivers gives the “misleading impression” that hands-free use is safe.