Beaming smiles, flawless outfits and royal waves — the Duchess of Cambridge and Meghan Markle have been out and about in the UK, seemingly competing for the title of People's Princess.

But is it a friendly rivalry or fierce competition?

The Duke and Duchess of Cambridge, both 35, and newly engaged Prince Harry, 33, and Ms Markle, 36, seem to be trying to one-up each other when it comes to their public appearances.

The royal family's glamorous next generation have been rubbing shoulders with the British public as they visited schools and cathedrals, reports News.com.au.

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Of course, the Duchess of Cambridge and royal-to-be Ms Markle have been front and centre of all photo opportunities.

Perhaps this is part of the Duchess and Ms Markle's campaign to be the next "People's Princess" — a term used to describe their late mother-in-law, Princess Diana.

The Duchess — who is pregnant with her third baby, due in May — was photographed at Bond Primary School, visiting the Wimbledon Junior Tennis Initiative program, and wearing bright pink at Coventry Cathedral.

Ms Markle took the train from London to Cardiff for her first official royal visit to Wales with Harry, where they attended Cardiff Castle and Star Hub, a leisure centre in Tremorfa.

Britain's Prince Harry and Meghan Markle watch a performance by a Welsh choir Cardiff Castle in Cardiff, Wales. Photo / AP
Britain's Prince Harry and Meghan Markle watch a performance by a Welsh choir Cardiff Castle in Cardiff, Wales. Photo / AP

Not only will former Suits star Markle gain a husband, title (most likely Her Royal Highness Meghan, the Duchess of Sussex) and royal obligations when she marries Harry in May, but also a sister-in-law — Catherine, the Duchess of Cambridge.

Meghan and Kate could become the next Princess Diana and Fergie, who had a very close and public friendship during their tumultuous marriages to Prince Charles and Prince Andrew.

Meghan Markle watched a game of Jenga during her visit to Star Hub in Wales. Photo / AP
Meghan Markle watched a game of Jenga during her visit to Star Hub in Wales. Photo / AP

So what will the stunning brunettes be like as sisters-in-law? Already, their tact in public is similar.

"It's such exciting news," Catherine said, on the news of Prince Harry's engagement to Ms Markle. "It's a really happy time for any couple and we wish them all the best and hope they enjoy this happy moment."

Meghan Markle attended a street dance class during her visit to Star Hub community and leisure centre in south Wales. Photo / AP
Meghan Markle attended a street dance class during her visit to Star Hub community and leisure centre in south Wales. Photo / AP

If the friendship between their predecessors, Princess Diana — William and Harry's late mother — and Fergie (aka Sarah, the Duchess of York) is anything to go by, they will be close, attending royal engagements together and taking family holidays.

"I really miss Diana. I loved her so much," Fergie said, in an interview with Harper's Bazaar in 2007 of her friendship with the late Princess.

"Diana was one of the quickest wits I knew; nobody made me laugh like her," she added.

"But because we were like siblings — actually, we were fourth cousins and our mothers, who went to school together, were also best friends — we rowed."

Prince Harry and Ms Markle will tie the knot at St George's Chapel, Windsor Castle, on May 19, in what is being billed as the society wedding of the year.