Dad - a smile for Damian?

Once the paternity of Damian Charles Hurley had been established by DNA tests, there appeared to be a certain

Now the war between Liz Hurley and film producer Steve Bing seems to be on again.

The actress and model flew to Los Angeles last week with a view to taking her four-month-old son to meet his father for the first time.

Miss Hurley, 37, had hoped her former lover would finally bond with the child after months of legal wrangling over his paternity.

But just days after her arrival, it appears the meeting is 'unlikely' to take place following a heated phone conversation between the pair.

'Liz was planning to introduce Damian to his father when she got to LA but it doesn't look like it's going to happen now,' said a source close to the couple.

'She has been there for almost a week promoting a movie and they still haven't come to an arrangement.

'They have spoken on the phone, but there is so much bitterness there that it's almost impossible for them to agree on anything.

'Neither of them know whether they will be able to work anything out now. It looks very unlikely.

'Steve and Liz have even been hanging around in the same places.

'I'm really surprised they haven't bumped into each other yet.

'That would be quite an embarrassment for both of them.'

Miss Hurley, who earned £2million a year as the face of Estee Lauder, is in Los Angeles promoting a comedy, Serving Sara, in which she stars with Friends actor Matthew Perry.

She and Damian flew from London to New York then finally to Los Angeles, where they are staying in a five-star hotel.

The actress, who has vowed to bring up her child alone, has said she wants no money from 36-year-old Bing, who is heir to a £300million property fortune.