Queen Mary is definitely behind the wheel, and with her hands on the steering wheel itself!
I very much doubt she drove, though. The King certainly didn't. The Duke of Windsor recalls in his memoirs being taken by taxicab by his mother, as a special treat for his birthday.
Later, Queen Mary had a notoriously bad chauffeur called Humphreys. She never complained or sacked him when he got lost enroute, which was frequently.
The Queen also had a penchant for picking up stray servicemen, many of them Americans stranded in the English countryside in need of a ride, which she would do with her thrifty nature, to justify the petrol expense. Her daughter, the Princess Royal, tells of a hilarious incident where they picked up an American airman in Gloucestershire.
He entered "with a jaunty, unpreoccupied air", sat down in the rumble seat inside one of the huge Daimlers Queen Mary used to use, which was directly facing Queen Mary, her lady-in-waiting, and her daughter, Princess Mary.
He turned his head slowly from the Queen, to Princess Mary, back to Queen Mary, then to Lady Cynthia Colville. A look of deep panic set into his eyes.
When Queen Mary, who wasn't at all shy with foreigners during the War, asked him what he did, he said he worked "in the Maternity Ward at a hospital". Men working at a maternity war, even with war scarcities, was HIGHLY unsual then.
After he left, much relieved not to be in the august queen's presence no doubt, Queen Mary shook her head, and laughed with that vulgar laugh of hers. "What on EARTH was an American serviceman doing helping out in a Maternity Ward!".
Humphreys probably got lost on the way back home.