Having visited the Aston Martin Heritage Trust a couple of days ago, I unexpectedly find myself able to give the following answer:
The car is Aston Martin A3, the third car to bear the name, built in 1921.
The photo was taken on the Isle of Man in May 1922 and the men are (L-R) Lionel Martin, Bertie Kensington-Moir, Clive Gallop and Count (Lou) Zborowski.