Billie Piper settles into motherhood on relaxing Miami break with baby Winston

Everyone else was swimming, tanning, or absorbed in a good book.

But Billie Piper only had eyes for her sleepy two-month-old son.

The actress spent the afternoon on a Miami beach enjoying baby Winston.

Beach babe: Billie Piper with her two-month-old son Winston on the beach in Miami

She gazed down at him as he lay on her lap, stretching his fat little arms in the warmth.

Miss Piper, 26, and husband Laurence Fox, 30, have been holidaying in the U.S. ahead of their first wedding anniversary on New Year's Eve.

An onlooker said: 'She looked relaxed, content and just generally very happy. Billie clearly adores her son.'

The pair are staying at the prestigious Shore Club hotel in Miami Beach.

My little angel: Billie only has eyes for Winston

They the afternoon on a public beach, ordering only soft drinks from the bar. Fox attempted to read and sunbathe, while Piper relaxed in the shade and cradled the child, who was wrapped in a sarong.

But the couple shared equally their parenting roles.

Mr Fox was very hands on changing nappies on the beach and taking their baby into sea.

Winston has only been seen a handful of times in public since he was born after a gruelling 26 hour labour by Caesarean section at the private Portland Hospital in London on October 21.

Mummy's boy: Billie cradles her sleeping son while husband Laurence Fox carries their belongings

But despite yesterday's scenes Billie's stay surely won't be all about the family.

The hotel is described as 'party central' at this time of year, charging a minimum of £450 a night. On New year's Eve it will see US rap mogul P Diddy will host one of the biggest parties in America.

All day yesterday he entertained his guests by sending fleets of bi-planes soaring above with a picture of him on a banner and the words 'I Am The King'.

Intriguingly however, Miss Piper has given fellow celebrity hotel guest Charlotte Church a wide berth.

Who's a pretty boy?: Smiling Billie only has eyes for her son

Daddy's boy: Laurence Fox plants a kiss on his son's little head

Mum's the word: Billie has given acting a break to concentrate on her son

Miss Church was seen yesterday parading around the Shore Club with a gaggle of girlfriends and without her partner, rugby star Gavin Hensen, or their children.

Billie, the star of ITV's Secret Diary Of A Call Girl has said she plans to take a break from acting to concentrate on her family.

But in recent months she has been tipped to become the first female Time Lord in Doctor Who, after lead David Tennant revealed he was quitting at the end of 2009.

Piper was a huge hit with fans and critics when she played the Doctor's assistant Rose Tyler when the show was revived for modern audiences in 2005.

Sleepy head: Winston has a stretch while a relaxed Billie enjoys a laugh

Tennant has given her his influential seal of approval and because the role is not free for another year, this could give Piper the time she needs to spend with her family.

Asked if Miss Piper could take on the role, he said a female Doctor was a distinct possibility.

'Why not?' he said. 'It's one of those parts any actor could bring something valid to, because it can be anything and it's a blank canvas every time.

Tennant will leave after completing four special episodes of Doctor Who to air next year.

Executives are looking for a new Time Lord for the fifth series, scheduled to broadcast in 2010.

Happy families: The actress and her husband pay close attention to Winston