In photos obtained by The Sun, the couple were dressed casually, with Prince Harry in a white shirt and a grey jacket with a beanie hat, while Meghan wore an oversized blue shirt under a black winter coat, leaving her brunette tresses loose.
An onlooker spotted the pair having dinner together, telling The Sun: "They tried to keep as low-key as possible and were sitting in a small snug area of the restaurant.But it wasn't a private area and they were happy to be seen... They only had eyes for each other."
The pair, who began dating in late 2016, have enjoyed several dates in the Prince's hometown, and were spotted attending the show The Curious Incident of the Dog in the Night Time at the Gielgud Theatre over Christmas.
They also went Christmas tree shopping at Pines and Needles in Battersea Park, and the shop's owner Sam Lyle spoke of his surprise at seeing them in his store. He told HELLO! Online: "We have looked after some of Britain's highest profile names for nearly 20 years but you could have heard a pin drop – or a needle – when Prince Harry and Meghan walked into the store. They were completely charming together and blissfully unaware that our jaws had hit the floor. They chose a gorgeous Nordmann Fir and walked away after exchanging Christmas pleasantries."
The pair are clearly enjoying their time together, and Meghan's co-star on Suits Patrick J. Adams recently opened up about their relationship. "I'm just super happy for her that she found someone that she seems to really be into," he said. "We don't talk about it a lot, obviously there is so much secrecy involved in something like that. I just sort of stay out of it, and I feel like a big brother."