They're enjoying a family summer holiday before preparing to move back to Los Angeles after a decade in London. 

And Gwyneth Paltrow certainly seemed to be enjoying having the opportunity to spend some quality time with her nearest and dearest as she stepped out on a stroll around The Hamptons with her daughter Apple on Thursday.

The 40-year-old actress looked effortlessly chic for her day out, teaming a simple cream shift dress with stylish and practical chocolate brown leather gladiator sandals.

Opting for a low-key look, the Oscar-winner wore her blonde hair tied back off her face, while sheltering her eyes from the sun with a pair of dark shades.

And little Apple, nine, certainly appeared to have inherited her mother's chic sartorial sense, looking every inch the mini-me as she stepped out with the Hollywood megastar.

The youngster looked fun and stylish in a blue striped playsuit, which she teamed with a pair of navy wedges for her day out in the sunshine.

Wrapping their arms around each other as they wandered through the upmarket area near New York City, the mother-daughter duo looked closer than ever.

The pair will need to get used to Stateside life after it was claimed Gwyneth and husband, Coldplay frontman Chris Martin, plan to make Los Angeles their home for the next two years after spending the last decade living in London.

It is believed the family will relocate to California in time for Apple and her brother Moses, seven, to start the new school year in September. 

A source told the Mail: 'Gwyneth has loved living in London but America will always be home and she wants to be closer to her family.

'Her mother and brother live in California and she plans to spend the next couple of years in Los Angeles while her children are young enough for their education not to be affected. She misses her family terribly and now is the time to move.

'Her children have English accents and once they start senior school Gwyneth says the family will likely return to the UK because she believes that the English education system is second to none.’

Rumours have been rife for months that the family was planning to move back to California after they forked out £6.6 million on an opulent new home in a private Hollywood Hills estate.

The 8,000 square-foot house in the exclusive Brentwood area is the most expensive in the couple’s property empire, which includes their £4.6 million home in North London, a £3.2 million penthouse flat in New York and a £3.4 million house in the Hamptons.