Appearing on Wednesday's One Show, the Top Gear host suggested that any worker on the strike should be shot "in front of their families".
Speaking today at the Women in Film and Television Awards, the 78-year-old TV presenter described his remarks as "outrageous" and "unforgivable".
She elaborated: "If I go round saying, 'I want Jeremy Clarkson's testicles cut off and fried in public', it's an insult.
"He's just a big mouth. I dislike the phrase, 'If I have given offence I apologise'. That's a cop-out. What you should say is, 'I give unqualified apologies'. That's what we'd like to hear."
Clarkson, who has since said that he is "happy to apologise", was reportedly given the go-ahead to make the joke by the BBC.
His comments have provoked 21,000 complaints from viewers, while trade union UNISON has called for the star to be sacked.
> Jeremy Clarkson 'intended to mock BBC with strike comment'