Rumours of an impending engagement heated up even further last week when Meghan Markle gave a gushing interview to Vanity Fair about her love for Prince Harry.

And now the Suits star, 36, is said to have achieved another important milestone in her relationship with the Prince - meeting his grandmother the Queen, reported the Daily Mail.

According to a report by Us Weekly, the actress was introduced to Her Majesty on 3rd September at Balmoral while the couple were visiting Prince Charles at nearby Birkhall.

"It went well," a source close to Harry reportedly told the magazine. "It'll no doubt be the first of many encounters.

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"She fits perfectly into the family. The difference in backgrounds means absolutely nothing."

The visit followed the couple's romantic getaway to Botswana to celebrate Meghan's 36th birthday, with the couple travelling north following their arrival back in the UK.

Harry apparently decided it was the perfect time to pay a visit to his father and grandmother as he hadn't yet been to Scotland where the Queen is usually joined by family members as she enjoys her summer holiday.

An introduction to his grandmother was the final step in making Meghan a permanent fixture in the family.

Reports suggest that the actress has already been introduced to the Duke and Duchess of Cambridge and is said to have forged a friendship with Princess Beatrice and her sister Eugenie.

She's also said to get on well with Prince Charles and Camilla who she's met on several occasions.

Meghan's introduction to the monarch has come about a lot more speedily than her potential future sister-in-law Kate's.

The Duchess of Cambridge was dating Prince William for five years before she met the royal at the wedding of Peter Phillips in 2008.

But with Meghan and Harry both in their 30s it's unlikely they will spend years dating before settling down.

Last week Meghan dropped the strongest hint yet that an engagement is imminent when she opened up about the relationship for the first time in an interview with Vanity Fair.

Prince Harry and Meghan Markle share a kiss. Photo / Rupert Hartley/REX/Shutterstock
Prince Harry and Meghan Markle share a kiss. Photo / Rupert Hartley/REX/Shutterstock

Speaking to contributing editor Sam Kashner, Meghan said: "We're a couple. We're in love.

"I'm sure there will be a time when we will have to come forward and present ourselves and have stories to tell, but I hope what people will understand is that this is our time."

Addressing their need for privacy, the actress added: "This is for us. It's part of what makes it so special, that it's just ours. But we're happy. Personally, I love a great love story."

When asked how she felt about the media frenzy that erupted after their relationship was revealed last year, Meghan replied: "It has its challenges, and it comes in waves - some days it can feel more challenging than others.

"And right out of the gate it was surprising the way things changed. But I still have this support system all around me, and, of course, my boyfriend's support."

She added: "I can tell you that at the end of the day I think it's really simple. We're two people who are really happy and in love."