William was the youngest child of Frederick Charles Williamson and his wife, Phyllis Hunter. His paternal grandfather was Sir Hedworth Williamson 8th Baronet. William had an older brother and a sister. His father died the year after his birth.
He was educated at Oundle and Matriculated in 1924. He graduated in 1928.
He became Managing Director of The Charlaw and Sacriston Collieries Limited of Newcastle upon Tyne.
On 12 December 1936, he married Diana Mary Lambton daughter of the Honourable Charles Lambton. They honeymooned in Madeira, arriving back in England on 4 January 1937. They had one son, Nicholas born in 1937, who succeeded his uncle in the baronetcy. The baronetcy expired with his death in 2000.
The Williamsons lived between their two residences, Whitburn Hall in County Durham and Appley Hall at Ryde in the Isle of Wight.
After Sandhurst, he joined the Northumberland Hussars which re-rolled in December 1939 to become the 102nd (The Northumberland Hussars) Lt. A.A./Anti-Tank Regt.
They were equipped with 36 x 2 pounder Anti Tank guns. They fought in Greece and in 1941 were attached to the 2nd Support Group of the 2nd Armoured Division in North Africa.
William was a Major when he was killed on 31 October 1942.
He is buried in the El Alamein War Cemetery Plot X. J. 12.
He is commemorated at the Royal Military Chapel, Sandhurst and on the War Memorial at Tow Law, County Durham.
Diana Williamson married in 1945, Patrick George Thomas Buchan-Hepburn, a Conservative Member of Parliament, created the 1st and last Baron Hailes in 1957. She died in 1980.