An eyewitness saw the pair taking the Express train from Heathrow Airport on Tuesday just days before Prince Harry paid tribute his mother’s loving memory.
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.”
The Suits actress is understood not to be filming for the television series, leading some to believe her visit could see Harry pop the highly anticipated question.
The loved-up pair are also said to staying at Prince Charles’ Scottish residence in Birkhall, less than eight miles from where the Queen is staying at Balmoral.
It is unclear if the actress has visited the Queen yet but a reported royal meeting could mark a major step in their relationship.
Prince Harry and Miss Markle have been together more than a year after the Sunday Express revealed their secret romance.
Before betting was suspended in March, Ladbrokes placed the odds Prince Harry and Meghan Markle becoming engaged in 2017 at 1/3 with a 2018 at 1/4.
Nicola McGeady of Ladbrokes said: “The sound of wedding bells is getting louder and louder as far as punters are concerned. This latest rush of bets has left us with no choice but to pull the plug on Prince Harry getting engaged this year.”
“As far as we are concerned, it’s no longer a case of will the couple get married but when, with 2018 looking highly likely.”
Miss Markle is believed to visiting to support her red-headed royal as he remembers the 20th anniversary of his mother death this week.
Prince Harry and William took a moment to read emotional tributes to Princess Diana on Wednesday after visiting a memorial garden in Kensington Palace with the Duchess of Cambridge Kate.
The Princes spoke to well-wishers as crowds gathered to pay their respect and said they were “thrilled” with the garden designed in their mother’s memory, as they recalled visiting it as small boys.
The Duke said he remembered “seeing the pigeons and squirrels”, adding: “We used to come here a lot.”
Recalling feeding the fish, the Duke said: “There never used to be this many in here,” before being told some of the koi carp were so old they would be the same ones.
The world was brought to a halt when the People’s Princess died on August 31, 1997 and admirers have already begun leaving floral tributes and photographs of the late royal at the gates of Kensington Palace, just as they did 20 years ago.
Sheltering from the heavy rain under an…