P/O Armstrong was born in Darlington, Conty Durham.
He entered the RAF on a short service commission and began training as a pupil pilot in January 1939.
After completing his training he joined 54 Squadron at Rochford towards the end of the year.

William was posted to 74 Squadron at Biggin Hill on 28th October 1940.
On 14th November he was shot down over Dover after destroying two Ju 87s. Whether he was shot by a Bf 109 or anti-aircraft fire is not known. He baled out and his aircraft (Spitfire P 7836) crashed onDover Road, Sandwich.

On 5th February 1941, William shared a Do 17 with three other pilots.
On 8th May, he destroyed a Bf 109.

William Armstrong as killed on 17th June 1941.

Flight Lieutenant William Armstrong is buried in Dely Ibrahim War Cemetery in Algeria. It is not known which unit he was with at the time of his death.