The Sherlock star, 53, has been dating the French actress, 30, since 2020, and on Saturday, was seen perusing the pieces on offer at a Dinny Hall store in north London.
Martin, 53, who played troubled police response officer Chris Carson, is up for a lead actor nod at the ceremony for his part in BBC One's The Responder.
The Sherlock actor, 53, and his French actress girlfriend Rachel Benaissa, 30, have been dating for around three years but are rarely seen together in public.