The birth of the boy - named Rudy - on Tuesday night was a month premature.

But both mother and baby are healthy, Frost's publicist said.

The pair have a film and theatre company

Frost already has two children, Iris, one, and Rafferty, five, with husband Law as well as 11-year-old Finley from her first marriage to ex-Spandau Ballet star Gary Kemp.

Frost is a regular subject in celebrity baby features and much has been made of her ability to keep working throughout her pregnancy.

Though enjoying a lower-profile acting career than Law, Frost has been acting and producing as normal.

As well as starring as a Jewish freedom fighter in the Warsaw ghetto-set film Uprising, she is producing World of Tomorrow, a sci-fi film to be shot next year.

Film romance

She has also spent time designing clothes for the French Frost label she co-owns and organising a catwalk show for London Fashion Week.

Law has recently returned from filming Cold Mountain with Nicole Kidman in Romania, another major role in a career that has included The Talented Mr Ripley, Enemy at the Gates and Wilde.

Frost and Law met on the set of British independent film Shopping when she was 24 and he was 19, and they have also worked together since.

Along with Trainspotting star Ewan McGregor they own a film and theatre company Natural Nylon.