Simon Glancey has submitted the following:

Sgt. Woolley was killed when Hawker Hurricane IV HV414 of 151 Operational Training Unit was lost on a training flight.

His death was reported in the Berwickshire News Tuesday 06/04/1943, page 3:

Paxton Sgt.-Pilot Killed
News was received by his parents in Paxton last week, that Sergt.-Pilot William A. Woolley, elder son of Mr and Mrs M. Woolley, Thorn Cottage, Paxton, has been killed on active service with the R.A.F. in India.

A native of Paxton, where his father is forester, at Paxton House, Sergt.-Pilot Woolley attended the local Council School and Berwickshire High School, and when he enlisted shortly after the outbreak of war, was attending a Forestry School. After a period of service with the Army, he volunteered for air-crew duties with the R.A.F., and gained his “wings” last year.

A younger brother, Archibald, was formerly with the R.A.F., but was discharged owing to ill-health; while his sister is a nurse at Western General Hospital, Edinburgh.

He is remembered in Berwick on B25.08

Coldstream History Society website
The CWGC entry for Sergeant Woolley