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The couple's visit comes after the duke celebrated the 10th anniversary of the Invictus Games at St Paul's Cathedral in London on Wednesday.
He smiled and waved at a crowd gathered in the sunshine outside St Paul's to greet him.
The service was attended by his uncle Earl Spencer - Princess Diana's brother.
Meanwhile, the King, whose cancer treatment is ongoing, met members of the public at a Buckingham Palace garden party a little over two miles away.
The two did not see each other, with the duke's spokesman saying the King's "full programme" prevented any meeting.
The BBC was also given exclusive access to Prince Harry's final engagement during his short trip to London - he was a surprise guest at a party hosted by the charity Scotty's Little Soldiers, which supports the bereaved children of military personnel.