June 14, 2018 at 08:56 AM EDT

The Duchess and the Queen have arrived!

Meghan Markle stepped out in northwest England on Thursday morning alongside the ultimate royal companion: Queen Elizabeth herself. The monarch wore a lime green suit dress by Stewart Parvin and a matching hat by Rachel Trevor Morgan, while Meghan wore a light beige pencil dress with a cape top by Givenchy (her wedding dress designer!).

The new Duchess of Sussex, 36, and the Queen, 92, disembarked in Cheshire, some 200 miles from London, via the royal train in Runcorn after spending the night aboard. The train is a favored travel option for the Queen and other senior royals because it allows them to work and relax en route.

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Not even a month since Meghan married Prince Harry on May 19, this is the first occasion the Queen has taken her new granddaughter-in-law on an official visit. The joint outing is “happening at triple speed” compared to Meghan’s predecessor, Kate Middleton, royals author Ingrid Seward previously told PEOPLE.

As the pair disembarked from the train, they were greeted by the Lord Lieutenant of Cheshire, David Briggs, who told Meghan: “I understand it is your first trip to the north of England.” She replied: “That’s correct. I’m very happy to be here.”

First on the pair’s agenda: the Mersey Gateway Bridge, where Meghan and the Queen met architects, planners and community representatives. They also watched a performance by local school children before Elizabeth formally opened the bridge.

Their next stop is the Storyhouse in nearby Chester, where they were set to meet a Syrian settlement group, watch a performance by the Fallen Angels dance company and catch a medley of songs from a current production of A Little Night Music.

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Their last appointment is set to be a lunch at Chester Town Hall with locals brought together by the council.

RELATED VIDEO: Why Meghan Markle’s Bare Shoulders at Trooping Would Never Be Allowed at Royal Ascot

The outing is seen as the Queen’s way of helping immerse Meghan into public royal engagements. “It is the way of the royal family—all part of the training and getting used to being in public life and under public scrutiny,” Elizabeth’s former press secretary, Charles Anson, tells PEOPLE. “Showing people the ropes is a high priority for the Queen.”

Seward, author of the recent biography of the Queen and Prince Philip, My Husband & I, adds, “The Queen knows the potential pitfalls of not giving [new members] a guiding hand. She can’t expect Meghan to know everything without being shown. I’m sure she feels Meghan needs a steadying hand in these early days.”

Meghan returned to public royal outings shortly after her secret honeymoon with Harry, when she joined in the annual celebration of the Queen’s birthday, Trooping the Colour, on June 9.

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