A pioneering flyer and aviation scholar, he piloted the first trans-Australia flight from Melbourne to Darwin in 1919, and afterwards laid the groundwork for the RAAF's air power doctrine.

[5] Wrigley trained as a pilot under the tutelage of Lieutenant Eric Harrison at Central Flying School in Point Cook, Victoria, before departing Melbourne on 25 October aboard a troopship bound for Europe.

[7] Having been promoted to captain, Wrigley was awarded the Distinguished Flying Cross for his "exceptional devotion to duty", in particular his persistence in pressing home an attack against enemy infantry on 29 October 1918 in the face of "intense machine gun and rifle fire"; the honour was promulgated in the London Gazette on 3 June 1919.

Accompanied by his mechanic and former schoolmate, Sergeant Arthur "Spud" Murphy, Wrigley departed Point Cook on 16 November and arrived in Port Darwin on 12 December, having travelled some 4,500 kilometres (2,800 mi) in forty-seven flying hours.

The men flew in a single-engined Royal Aircraft Factory B.E.2, with no radio, over unmapped and often hazardous terrain, and surveyed seventeen potential landing fields along the way.

[12][13] Wrigley considered the choice of Murphy as his cohort "a particularly happy one" but called the aircraft they were assigned "an obsolete type, even for training purposes", while conceding that "it was structurally sound and airworthy".

[13][15] Such was the perceived danger of the expedition that while making preparations for the flight back they received a telegram from the Defence Department ordering them to dismantle the B.E.2 and return with it by ship.

[14] On 1 January 1920, Wrigley transferred to the Australian Air Corps (AAC), a temporary organisation formed by the Army following disbandment of the wartime AFC.

Taking off from RAAF Station Richmond in an Airco DH.9, Wrigley and his co-pilot were in the air for six hours and covered 345 miles (555 km) before a broken fuel line forced them to land for repairs; they completed the journey the following day.

[26][27] In May 1939, Wrigley served as the senior expert assessor on the panel of an inquiry into three recent accidents involving Avro Ansons; the full report handed down in October found that training on the type followed the syllabus, but that pilots needed more practical experience in dealing with in-flight incidents, as human error was the likely explanation for at least one crash.

1 Group was formed under Wrigley's command in Melbourne on 20 November 1939, to oversee the operations of air bases and units in Victoria, South Australia, and Tasmania.

[34] He believed that recruiting servicewomen was essential to augment the many ground staff required to support the war effort, and considered that although such an organisation should be constitutionally separate from the RAAF, its members should be closely integrated within the current force structure.

[3][36] On 21 May, he selected Berlei executive Clare Stevenson as WAAAF Director, passing over temporary appointee Mary Bell, wife of a serving RAAF group captain.

[38][39] Wrigley's promotion to acting air vice marshal was announced in May 1941, making him only the third member of the RAAF—after Richard Williams and Stanley Goble—to attain this rank.

[46] The role had little influence on the deployment of Australian personnel for the air offensive in Europe, who were subject to RAF policy and strategy even when they belonged to RAAF squadrons.

[24][47] According to the official history of Australia in the war, Wrigley and his predecessors could hardly do more than "retard the centrifugal forces affecting Australian disposition, and repair the worst administrative difficulties arising from wide dispersion".

[48] Wrigley became a familiar and popular figure for the thousands of Australian airmen who passed through London during the war, and was known to take off his jacket and tend bar at Codgers, the headquarters' watering hole.

The official history contended that "for the most part Australia was still left chasing a dream rather than a reality", as many clauses in the agreement were "subject to operational exigencies" and to be adhered to only "as far as possible".

[53] The end of hostilities in Europe on 7 May 1945 raised a major logistical challenge for Wrigley as the senior officer responsible for some 13,500 RAAF personnel spread across Britain, the Mediterranean, and the continent, only a minority of whom were in nominally Australian squadrons, the bulk serving with RAF establishments.

"The task was energetically met", according to the official history; fewer than 1,000 RAAF personnel remained in RAF units by 1 September, although repatriation continued through into the new year.

[54] Wrigley was forcibly retired from the RAAF in 1946, along with other senior commanders and veterans of World War I, ostensibly to make way for the advancement of younger and equally capable officers.

[1] An "inveterate note-taker" according to friends, during his career Wrigley compiled extensive documentation concerning the theory and practice of air power, on which he lectured among his colleagues in the RAAF during the 1920s.