The Queen and Meghan attend a day of engagements together in Chester

She may only have been a member of the royal family for a few weeks, but Meghan Markle is already getting stuck into working royal life, carrying out a series of engagements with none other than the Queen herself.

The newly appointed Duchess of Sussex and the monarch stepped out in Cheshire this week, for their first ever official engagement just the two of them.

The pair looked relaxed and happy as they disembarked from the royal train for their day of engagements - and both royals looked equally as stylish.

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Meghan opted for a simple cream Givenchy dress - the first time she's worn the designer since choosing them to make her now world-famous wedding dress.

Her Majesty donned one of her trademark suits in a striking green hue. Some have speculated that there was a special significance behind the Queen's colour choice for the day, with many praising the monarch's 'choice' to, 'wear green for Grenfell'.

It has been one year since the fatal fire ripped through a tower block in West London claiming 72 lives, and the Queen and Meghan began their day of engagements with a 72-second silence to pay respect to the victims.

The colour green has come to represent the campaign to remember the victims of the fire, leading many to say that the Queen picked her outfit as a way to pay tribute to those who tragically lost their lives.

After the 72 second silence, Her Majesty and Meghan attended the opening Mersey Gateway Bridge, in Chester. They looked to be getting along like a house of fire, chatting and laughing as they sat down to watch a dance performance.

Meghan and Queen Elizabeth then headed over to the city's Storyhouse theatre - a sweet nod to Meghan's dramatic roots.

Then, the Queen and the Duchess attended a lunch at Chester Town Hall, after a jam-packed morning of engagements.

Meghan's Chester engagements mark the first time she has ever undergone a series of official royal duties without Prince Harry by her side - and the first time she has ever undertaken them with just Queen Elizabeth II.

Previously, the Duchess has been on engagements with the Queen - including a Commonwealth Day service. However, there, she was joined by other members of the royal family too.

Meghan has been invited on her first engagement with the Queen relatively quickly, by royal standards. In contrast, the Duchess of Cambridge didn't head on her first official engagement with the Queen until almost a year after she and Prince William married.

In March 2012, she joined the monarch to travel to Leicester by train from Kings Cross St. Pancras Station as part of the Queen’s Diamond Jubilee tour.

Aside from similarities between the two Duchess' first days out with the Queen such as the chance to catch up with Her Majesty over a cup of tea whilst traveling by train, Meghan and Kate's first solo outings with the monarch include another parallel - they both seem to be able to make the Queen laugh!

Meghan was seen giggling away with the Queen over a private joke during their day in Cheshire, just as Kate was seen doing six years ago.

(Image credit: Getty Images)

It seems the Duchess of Sussex is keen to get stuck in to royal life just like the Duchess of Cambridge - and clearly, she's learning from the best on her first solo engagement.

Meghan and Harry only recently returned from their two-week honeymoon, following their 19th May nuptials.

The couple attended the Trooping the Colour ceremony shortly after returning home, which is held in order to celebrate the Queen's birthday. The newlyweds joined the rest of the family on the balcony of Buckingham Palace.