The photograph showed the 95-year-old monarch wearing a headscarf and sunglasses behind the wheel of the car.
In October, the monarch was forced to cancel some planned engagements and spent a night in hospital for an unspecified, although not Covid-19 related ailment, her first such overnight stay since 2013.
Watch: Queen advised to rest for the next two weeks
One of those engagements she was forced to pull out of was a reception to mark the opening of the United Nations climate change summit COP26, which was getting fully underway on Monday.
The Queen, who is known for her robust health, has still carried out a number of virtual audiences by videolink, in which she has appeared well and cheerful.
Despite ruling out attendance at the Festival of Remembrance at the Royal Albert Hall on November 14, Buckingham Palace said the head of state has the “firm intention” of leading the nation in honouring the country's war dead on Remembrance Sunday the next day.
In a statement on Friday, the palace said: “Following on from their recent advice that the Queen should rest for a few days, Her Majesty’s doctors have advised that she should continue to rest for at least the next two weeks.
“The doctors have advised that Her Majesty can continue to undertake light, desk-based duties during this time, including some virtual audiences, but not to undertake any official visits.
“Her Majesty regrets that this means she will be unable to attend the Festival of Remembrance on Saturday November 13.
“However, it remains The Queen's firm intention to be present for the National Service of Remembrance on Remembrance Sunday, on November 14.”
There will be concern for the Queen given her advanced years, but medics see the period of rest as a sensible precaution.
The Queen appeared cheerful and in good humour when she hosted a virtual presentation ceremony on Thursday, awarding the Queen's Gold Medal for Poetry 2020 to poet David Constantine.
Watch: A closer look at the Queen's busy October