When people engage in online rows, known as "flame wars", they often do battle from behind the cloak of anonymity. Yesterday Michael Winner tried to douse a spectacular and very public conflagration sparked by a dispute with Victoria Coren.

The film director and food critic tweeted that Ms Coren, the broadcaster and writer, was "rude beyond belief" and "not well brought up" after she made a late-night phone call to the Winner residence in London. Ms Coren was so shocked by a series of "pitiful" tweets from Winner's account that day, which marvelled at her breasts, she believed his account might have been hacked into by an adolescent boy.

A furious Winner confirmed that the tweets were his, and objected to a "stranger" calling him so late. He tweeted: "Victoria Coren is RUDE. how dare she call at 10.25pm; this is outside courtesy hours. I don't know her, don't want to know her, won't speak."

A further dismissive tweet about Ms Coren's late father, Alan Coren, the distinguished journalist, inevitably caused Giles Coren, her brother and a regular tweeter, to enter the fray. He inquired: "Why are you badmouthing my family? Why are you insulting my dead father? And when did I 'stab you in the back?' "

Winner has become the latest celebrity to be tempted by Twitter's ease of use into starting spats in a new age of web warfare. Alan Sugar called Kirstie Allsopp a "lying cow" in a tweet, after the property show presenter described his behaviour during a Celebrity Apprentice special as "shockingly uncharitable".

Winner, whose Twitter page warns that he is "a bad-tempered, totally ridiculous example of humanity in deep shit", told The Independent he had accepted an apology from Ms Coren. "She got very upset and rang me at 10.25pm at night and that was appalling. It wasn't a very serious matter. She apologised and the matter is now closed. I didn't seize on Victoria's bosoms, my followers did. Their remarks were terribly funny. She should be happy that people are writing nice things about her bosoms." Ms Coren said: "I never really argue with anyone so it's surprising to find that I'm one of those people having a Twitter row with a celebrity. I assumed it was an impostor.

"He only had 6,000 followers and the tweets were so weird and misspelt, I thought they were satirical." She added: "The stuff about my breasts was just pitiful and silly. But he made a rude remark about my father, who isn't here any more, and that's not OK. That's the only thing that made me really angry."

And Ms Coren fired off a parting shot. "I sort of admire him that at his age – he must be nearly 90 – he's so open to new experiences. Firing off 20 tweets about my breasts in 10 minutes is something you'd expect from a 14-year-old having his first can of cider."

Winner, 75, believes his every thought should be in the public domain, if only because "I don't know how to send a direct message". With the Coren affair closed, he has settled on a new target. "I've been tweeting about Esther Rantzen today. Nobody likes her. Twitter is a wonderful way of speaking directly to people without all the peripherals. It's ridiculous that some people take it seriously."