Although croquet had been played in Victoria (at Kyneton) since at least 1866, the Victorian Croquet Association was not formed until 1914 and affiliated with the (English) Croquet Association in 1917. After this affiliation it acted as the governing body in Australia and was so recognised by the Croquet Association - at this time, and for some time after, Victoria was the strongest croquet state.
Immediate attempts were made to arrange a challenge match between the two countries, but World War 1 intervened and it wasn't until Australia issued a challenge in 1924, which was accepted by the Croquet Association, that a test series was arranged to take place in England in 1925.
Victoria contacted the other states, requesting nominees for the team, which were received from Queensland and New South Wales, although the NSW nominee later withdrew, and the Queensland representative, Mrs H Dinsdale accompanied the team as the Reserve.
In February 1925, Mr MacPherson Robertson's offer of a silver mounted shield for international competition was accepted by the Victorian Croquet Association and was despatched, following the team, which was already in England. That challenge match was won by England. The return challenge, held in Australia in 1927, was won by Australia.
New Zealand joined the competition in 1930, but England did not compete. All competed in 1935, but New Zealand did not compete in England in 1937. Since then, all nations have competed, with the United States of America joining in 1993.
More information about Sir Macpherson Robertson can be found on Wikipedia