The pair were photographed on a boat while holidaying with family in Mykonos.
The billionaire retail tycoon Sir Philip's daughter, Chloe, 27, last month gave birth to her first child with Meeks, a baby boy called Jayden Meeks-Green.
The Topshop heiress was also pictured relaxing on the boat, alongside her mum Lady Tina Green.
Baby Jayden is Chloe's first child, although her model boyfriend – nicknamed "hot felon" after his mugshot went viral – already has a son with estranged wife Melissa.
Meeks, 34, was jailed in 2009 for stealing and again in 2014 for gun law violations. The pair have been dating since last year.
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