Whitcombe began his career at Came Down Golf Club in Dorset and served in the British armed forces during World War I. He was the professional at Parkstone Golf Club from 1 January 1928 until his death in 1957. He finished runner up to Henry Cotton in the 1937 Open Championship at Carnoustie, and in 1938 he won the Open at Royal St George's. His two older brothers Ernest and Charles were also professional golfers and all three played for Great Britain in the Ryder Cup, with Reg making his appearance in 1935.
|The Open Championship||T20||T14||CUT||T23||T45||T13||T17||T17||T7||T16||T34||T8||2||1||T3|
|The Open Championship||NT||NT||NT||NT||NT||NT||T14||T13||T18||CUT||CUT||CUT|
NT = No tournament
CUT = missed the half-way cut
"T" indicates a tie for a place
Green background for wins. Yellow background for top-10