Members of the public claim to have seen the couple on the public transport on Tuesday, just days before Harry paid tribute to his mother.
The source said: “The pair wore baseball caps and sat in the first class carriage, reading magazines and chatting quietly.
“[Meghan] was smiley and giddy looking.”
This sighting has sparked hopes the the pair might be engaged very soon
First class tickets on the Heathrow Express cost around £55, but the pair made sure they enjoyed what luxury the train has to offer.
According to the sources Meghan was not wearing an engagement ring.
The reports are very contrary to recent news that Prince Harry picks Meghan up in his car from the runway to protect her from the public and paparazzi.
The Prince has pulled strings to ensure the American actress can walk straight from the plane steps to his waiting Audi RS6 when she lands in London, bypassing the usual passport queues.
Princess Diana died 20 years ago yesterday in a car crash in Paris.
Diana married the Prince of Wales at St Paul’s Cathedral and becomes HRH the Princess of Wales and a future Queen. Express.co.uk remembered her life in pictures.