The pair is believed to have hit it off while holidaying on Branson's Necker Island in the Caribbean – a trip that ended in disaster when the Great House was engulfed in flames after being struck by lightning.
Ned, 33 - who changed his name from Abel Smith to suit his role at Virgin Galactic – recently split with wife Eliza Cowdray. He is said to have retreated to the island to lick his wounds.
This week he and Kate were spotted laughing together in London, sparking speculation that their friendship has become something more.
A source told The Sun, 'Ned was heartbroken and went to Necker to take his mind off things. But when Kate came out they really hit it off. They had met before on the island but both were in relationships.
'When they left, they travelled to New York to be together.
'Kate has been so happy. At the Emmys all she did was keep showing people pictures of Ned and talking about him.'