The former cabinet minister David Mellor has publicly apologised for verbally abusing a London cab driver after a visit to Buckingham Palace with his partner, who had just been awarded a CBE.

The QC and ex-Conservative MP said he had a case for justifying his annoyance, but threw it away with his foul language.

Mellor issued the apology for his rant during the first phone-in session on his LBC radio show since the incident, saying he can’t and won’t defend his actions.

In his outburst, recorded on a mobile phone, Mellor called the black-cab driver a “sweaty, stupid little shit” during an argument about the route he wanted to travel after picking up Mellor and his partner, Lady Cobham, from her investiture ceremony.

He said: “You’ve been driving a cab for 10 years, I’ve been in the cabinet, I’m an award-winning broadcaster, I’m a Queen’s Counsel. You think that your experiences are anything compared to mine?”

Mellor told the driver to “fuck off” and said he would name him and discuss the incident on his LBC radio show.

Mellor began the show on Saturday by telling listeners he was “really, really sorry” and promised to make a substantial donation to the Licensed Taxi Drivers Association’s Christmas charity appeal.

“I can’t think what possessed me to lose it with that cabbie the way I did,” he said. “OK, I had a case, but I threw it away by the way I spoke and I’m really, really sorry about that, and I especially want to apologise to you, our listeners, for trying your patience and risking my own credibility with you by speaking the way I did.

“Anyway, it’s water for me at the next celebratory lunch, I’ve definitely made that decision.”