After arriving at the station shortly after 10.30am the pair were escorted towards the car, with footage suggesting Meghan was told to go in ahead of the Queen - but the monarch, apparently oblivious, went in first instead.
A flustered Meghan then stepped in to suggest she go in first instead, prompting the 92-year-old to stand back before settling into her preferred seat, where an aide covered her with a blanket to keep warm.
Etiquette expert William Hanson told MailOnline: "The Queen always sits behind the driver.
"This is just a case of habit not protocol (protocol actually says the most important person sits diagonally behind the driver) but the Queen has always preferred being directly behind whoever is driving her.
"Meghan was probably not aware of this and the royal household may have forgotten to brief The Duchess of Sussex in this nuance.
"It was, however, a considerate gesture from the Duchess of Sussex to consider where the Queen would like to sit."
The pair travelled overnight on the royal train for a day of engagements including the opening the Mersey Gateway Bridge and Storyhouse in Chester, arriving at Runcorn on Thursday morning.
The awkward exchange comes as Meghan continues to adjust to life as a full-time royal.
Last weekend, the Duchess was seen looking to her husband for reassurance as she joined senior royals on the balcony of Buckingham Palace for the Trooping the Colour flypast.
According to Mirror Online, a lip-reading expert has claimed that Harry asked his wife if she was OK during a private exchange between the newlyweds, to which she anxiously responded: "Yeah".
A short while later, Meghan appeared to admit she was feeling "nervous" as she made her balcony debut in front of huge crowds who had gathered on The Mall to catch a glimpse of the royals.
In another moment captured on camera, Meghan appeared to discreetly ask Prince Harry, 33, whether it's time to curtsy as Queen Elizabeth arrives.
In the video, Meghan, still smiling and looking ahead, appears to mouth "Do it?" in direction of her husband, who seems to reply "Yes" before promptly bowing his head.
The duchess, standing right behind Kate Middleton and next to Harry, then curtsies along with the rest of the royal family as a sign of respect for the 92-year-old monarch.
Protocol dictates that royals must curtsy in front of the queen when they see her for the first time of the day.