In recent weeks, Meghan and Harry have faced criticism for insisting on keeping their son Archie's christening completely private, and refusing to reveal the names of his godparents.
A week later, Meghan made a controversial "private" appearance at Wimbledon with two friends, and caused a stir when bodyguards told fans not to take pictures of her.
The Duke and Duchess met the cast and crew of The Lion King during a line-up inside the Odeon in Leicester Square, including Pharrell Williams.
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The exchange began with Harry laughingly admiring Pharrell's tuxedo jacket and shorts combination, and the musician doing a jokey curtsey for the prince.
"I love the look," laughed Harry, pointing to the eccentric outfit.
Royal fan Pharrell took the opportunity to praise the royal couple, telling them: "So happy for your union. Love is amazing. It's wonderful."
He added: "Don't ever take that for granted, but what it means in today's climate, I just wanted to tell you it's so significant for so many of us. Seriously."
Meghan thanked the musician, saying: "That's so kind of you to say."
Pharrell continued: "It's significant. I cheer you guys on."
Reaching out to touch him on the arm, the Duchess admitted: "They don't make it easy."
Pharrell added: "So you understand the significance. It's beautiful."
The premiere comes at the end of a difficult period for Meghan, who has faced widespread backlash over her privacy demands.
Meghan was branded "childish" and "a control freak" by former world champion Sally Jones, 64, following an appearance at Wimbledon last week, as she flaunted dress codes at the event while her security told fans not to photograph her.
The controversy came just days after Meghan and Harry faced a public backlash for insisting on keeping their son Archie's christening completely private, and refusing to reveal the names of his godparents.
The Duchess donned a stunning £3454 mid-length black gown by designer Jason Wu for the occasion, with a sheer panel across the top of the bodice and sleeves. The royal carried a small black satin clutch bag from Gucci costing £1680, and finished her outfit with a pair of embellished sling back black pumps by Aquazzura, costing £640.