The video footage, captured by cameras mounted on the front and back of Mr Vine’s bike, apparently shows Shanique Syrena Pearson, 22 of Vauxhall, sounding the horn of the black Vauxhall, getting out of the car to confront Mr Vine and swearing repeatedly.
There are shouts of “Get the f*** out of the road” and Mr Vine’s bike is apparently kicked, also made a gun sign at him during the row in Kensington on 26 August 2016.
She was convicted of driving without reasonable consideration for other road users and using abusive or insulting words or behaviour.
Her appeal will be heard on 18 April.
Pearson, who has a number of previous convictions including assaults and theft, had been warned she could be jailed as she was subject to a suspended sentence when the argument happened.
She has admitted driving an unlicensed vehicle.
The mother-of-one was to be sentenced at Isleworth Crown Court but the hearing was postponed pending her appeal.
The footage was viewed more than half a million times online and sparked a debate about the safety of cycling in London.
Mr Vine, a prominent cycle safety campaigner, has recorded his cycle commute to work since being knocked off his bike in 2014.
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