Parr was born in Lichfield Grove, Finchley, he lived most of his life at 52 Lodge Lane, North Finchley, the youngest of the eleven children of Edward and Alice Parr.

On leaving school, he took a job as a butcher's boy, and then as golf caddy at North Middlesex Golf Club. Then, like many other young men of the time, he was attracted to the army as a potentially better way of life, and one where he would at least get two meals a day and a chance to see the world. The 5'3" tall Parr joined the 4th Battalion of the Middlesex Regiment in 1912, aged 15, but claimed to be 18 years and one month old to meet the minimum age requirement.

Private Parr specialised in becoming a reconnaissance cyclist, riding ahead to uncover information then returning with all possible speed to update the commanding officer.

At the start of World War I in August 1914 Parr’s battalion was shipped from Southampton to Boulogne-sur-Mer, France. With the German army marching into Belgium, Parr's unit took up positions near a village called Bettignies, beside the canal running through the town of Mons approximately 8 miles (13 km) away.

On 21 August, Parr and another cyclist were sent to the village of Obourg, just north east of Mons, and slightly over the border in Belgium, with a mission to locate the enemy. It is believed that they encountered a cavalry patrol from the German First Army, and that Parr remained to hold off the enemy whilst his companion returned to report. He was killed in the ensuing rifle fire.

Parr is buried in the St Symphorien military cemetery, just southeast of Mons. Coincidentally, his grave faces that of George Edwin Ellison, the last British soldier killed during the Great War.