Basil was the youngest of the three sons of James William and Gertrude Amy Caygill. He was born in Headingley, Leeds and baptised at All Hallows Church on 1 May 1904. His father was a teacher of pianoforte and singing. The family lived at 9 Winstanley Terrace, Leeds.
He was educated at Leeds Grammar School and matriculated in 1922. He was awarded an Exhibition in Natural Sciences. He played in the Rugby XV.
His father died in 1927.
The Degree of Bachelor of Medicine was conferred on him at Congregation of the University of Oxford on 17 October 1929. He was, also, M.R.C.S., L.R.C.P. [London]. He was in general practice at Crown House, Retford. Nottinghamshire.
On 21 July 1939, he sailed from Liverpool on the Duchess of Bedford and was one of eleven passengers entering the United States at St. Albans, Vermont. It seems that he was on a holiday as he sailed out of Montreal on the same ship, returning to Liverpool on 4 August.
He was a Captain in the Royal Army Medical Corps when he died on 6 February 1945.
He was buried in the Basra War Cemetery, Plot 7 R 4.
His oldest brother, Leonard Edward Caygill was Assistant Director, Directorate of Civil Aircraft Research and Development, Ministry of Supply during the war.