Just four weeks after a blind date with US actress Meghan Markle that left him "beautifully surprised", Britain's Prince Harry took his wife-to-be on a trip to Botswana to camp under the stars in his tent.

Harry, 33, Queen Elizabeth's grandson and fifth in line to the British throne, and Markle, 36, best known for her role in the US TV legal drama Suits, got engaged this month at their cottage in London over a roast chicken dinner.

In their first broadcast interview since announcing the news earlier on Monday, Harry and Markle held hands as they discussed the moment of their proposal and their courtship.

"It was just an amazing surprise. It was so sweet and natural, and very romantic. He got on one knee," Markle said. "I could barely let you finish proposing. I said, "can I say yes now?""

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Harry said that he had not watched the show which made Markle's name, and Markle too was relatively unfamiliar with Britain's royal family before meeting Harry.

"I had never watched Suits, I had never heard of Meghan before and I was beautifully surprised when I walked into that room and saw her. I was like, 'OK well I'm going to have to really up my game here'," Harry said.

Harry and Markle, who is a divorcee, met in July 2016 after they were introduced through a friend who set them up on a blind date. They are due to marry in the British spring next year.

Markle said she was not prepared for the level of attention their relationship would get.

"I did not have any understanding of just what it would be like," she said, saying there was a misconception that because she was an actress she would be used to being in the media spotlight.

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In his office's warning to the media, Harry referred to the sexism and racism directed at Markle, whose father is white and her mother African-American.

"Any the end of day I'm really just proud of who I am and where I come from and we have never put any focus on that," she said. "We were just hit so hard at the beginning with a lot of mistruths."

Markle said she had met the Queen, who she said was an incredible woman. Harry quipped that the Queen's corgis had taken to her straight away despite barking at him for years.

Markle showed off her three-stone engagement ring set in yellow gold, which features a diamond from Botswana and two other gems from the collection of his mother, Diana, who died in a car crash in 1997.

READ MORE: Prince Harry and Meghan Markle announce engagement

"It's beautiful, and he designed it. It's incredible ... obviously not being able to meet his mum, it's so important to me to know that she's a part of this with us," Markle said, turning to Harry as she spoke about the ring.

"It's incredibly special to be able to have this, which sort of links where you come from, and Botswana, which is important to us, it's perfect."