Hampshire first appeared amongst Bira, Villoresi, Tony Rolt, Raymond Mays, Peter Whitehead, Leslie Brooke and Reg Parnell in the 1939 Nuffield Trophy at Donington Park.

However, the Maserati 6CL which he was driving, formerly owned by Arthur Dobson and re-engineered into an 1,100 cc (67 cu in) car, only managed a few laps, retiring with a melted piston.

On the whole, 1948 was more fruitful: he finished second in his Delage 158L in the 1948 British Empire Trophy at Douglas, Isle of Man, and seventh in the Zandvoort Grand Prix in the Netherlands.

He took pole position for the non-Championship Jersey Road Race in the Scuderia Ambrosiana Maserati 4CLT, but his maiden Formula One win eluded him when the car's magneto failed.

He competed in the 1951 24 Hours of Le Mans race in a works Aston Martin DB2 where, along with his friend, Reg Parnell, he finished third in class and seventh overall.