The family moved to Aberdeen in Scotland the year after Godley's birth and then to London in 1873 where he entered the Royal Naval School as he intended to join the Royal Navy. However, after a few years, Godley reconsidered his future and chose to pursue a career with the British Army. To ensure he was adequately educated to qualify as a gentleman cadet for the Royal Military College, Sandhurst, he was enrolled at Haileybury College in 1879. The following year, when he was 13, his father died leaving his mother to raise and educate four children with limited financial resources.