Brickhill was born in Melbourne, Australia to journalist George Russell Brickhill (26 January 1879 to 1964) and Izitella Victoria Brickhill (nee Bradshaw). He was the third son of the couple's five children, the others being Russell (1913 - ), Ayde Geoffrey (1914 - ), Lloyd (1918 - ) and Clive (1923 - ). When Brickhill was 11 the family moved to Sydney where he was educated at North Sydney Boys High School. A classmate, and friend, was actor Peter Finch.
Brickhill left school in 1931 as his father had been made redundant by the depression. While his other brothers continued with their education it was necessary for Brickhill, who was regarded as the least academic of the children to get a job to assist his older brother Russell in bringing money into the family. He was sacked from his first two jobs due to his stutter. He then got a job as office boy and then lift boy at the Adelaide Steamship Company. That job didn't last long as Peter Finch who was by now working as a copy boy was able to convince a news editor at The Sun to interview him in 1932. Brickhill was hired as a copy boy and within a year promoted to cadet journalist. Within a few years he had worked his way up to journalist and by 1940 was a sub-editor.
Brickhill was initially unimpressed by war fever, until the shock of the invasion of France and subsequent withdrawal from Dunkirk, coupled with boredom with his deskbound sub-editor job, caused him to enlist on 6 January 1941 with the Royal Australian Air Force (RAAF). His flight training commenced in March 1941 at the Number 8 Elementary Flying Training School at Narrandera, New South Wales as undertaken in Australia Under the Empire Air Training Scheme, Brickhill then undertook advanced training as a fighter pilot in Canada and the United Kingdom, before being assigned to No. 92 Squadron RAF, a unit equipped with Spitfires and part of the Desert Air Force in North Africa.
On 17 March 1943, he was shot down over Tunisia and became a prisoner of war. he was flown to Italy on 23 March and then sent by train to Germany. After initially being held at the Dulag Luft at Oberursel, a Luftwaffe's central receiving and interrogation station for captured enemy airman he was sent to Stalag Luft III, in Silesia, 150 km southeast of Berlin, arriving there on 4 April 1943. Brickhill became involved with the camp's escape organisation initially as a lookout or "stoogie", before volunteering to work as a digger on the "Tom" tunnel". However he developed claustrophobia. As a result he was eventually reassigned and was put in charge of security for the forgers. Because of his claustrophobia and the risk that he would panic and block the escape of others behind him he was not allowed to take part in the mass escape attempt, which is today known as "The Great Escape".
Following the announcement of the murder of the escapees who had been recaptured following the Great Escape, Brickhill became determined to document the event. Discussing the subject with fellow prisoner Conrad Norton, they identified that many of their fellow prisoners had other tales of daring escapes, and that they could provide the possibility of publishing a book following the end of the war. As Brickhill had been involved in "The Great Escape" he concentrated on that story while Norton collected individual tales. As prisoners were forbidden from writing anything other than letters and postcards, they collected every piece of paper they could find and, writing in as small a hand as possible, they collected stories and hid them from the guards.