They later hit up the elegant Contemporary, which hosted the Terrence Higgins Trust World AIDS Day charity fair.
Markle has given up her roles with World Vision and UN Women to act as patron for the Royal Foundation, set up by Harry and his brother Prince William to support charities, but aid groups urged her to use her elevated fame to engage the public.
The 81-year-old is well-known for handing bags of Haribo candies to Harry, and first presented his father, the Prince of Wales, with two bags - the other for brother William - 20 years ago.
Queen Elizabeth's grandson Harry, 33, now fifth-in-line to the throne, and US actress Markle, 36, best known for her leading role in USA legal drama "Suits", announced their engagement on Monday, igniting a trans-Atlantic media frenzy.More news: How to Fix: macOS High Sierra Flaw Allows Admin Access Without Password
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"As long as they're happy, that's all that matters".
Kensington Palace hasn't announced any more engagements for the couple yet.
The couple, who got engaged earlier this month at the cottage they share in the grounds of Kensington Palace in central London, are to be married next May in St George's Chapel at Windsor Castle, the family home of British kings and queens for nearly 1,000 years.
On Tuesday it was confirmed that Markle will step down from her charitable duties working with World Vision Canada and as a United Nations women's advocate so that she can start her new royal life with a clean slate.
You're live on This Morning Harry" but as she put the microphone in his face, he completely swerved her and said: "'I'm just going to go this way!'
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