Next time it happens go to the back of his cab and take down his PCO number - that's the number on the white plate, not the registration number.
Then make a formal complaint to the PCO (Public Carriage Office: https://www.tfl.gov.uk/tfl/contact/pco/default.aspx). If you don't come over like a self-righteous cyclist, they will take a complaint very seriously, and cabbies have been known to be disciplined (fined whatever) for unsocial behaviour.
Do it. And if you can get a witness, more's the better.
I've had a black cab and some private vehicles run into my back wheel.
I've had a black cab and some private vehicles run into my back wheel.
As for the PCO, they do nothing with traffic incidents.
http://www.londonfgss.com/post36559-57.html