He won the 1936 Open Championship at Royal Liverpool Golf Club in Hoylake, Merseyside, England[2] and played for Great Britain in the Ryder Cup in 1933, 1935 and 1937.

His family had close ties to Royal Ashdown Forest Golf Club in Sussex, where he served his apprenticeship under head professional Jack Rowe.

As a tournament player, he came into prominence in 1931 when he won the News of the World Match Play at Royal Mid-Surrey Golf Club, beating Mark Seymour in the final and receiving £300 in prize money.

On 20 May 1933, Padgham took part in an exhibition match against Percy Alliss, as the main event at the opening of the reconstructed West course at Sundridge Park Golf Club, in the south east suburbs of London, near Sevenoaks in Kent.

On that final day, he had to break into the locked Hoylake pro shop to retrieve his clubs for an early tee time, but seemed completely unperturbed by the incident.

During the war, Padgham joined the full-time Special Police and part of the club house and golf course at Sundridge Park was used for military purpose.