How quickly do acts of gallantry which result in the individual being Mentioned in Despatches get published in the London Gazette?

My query relates to Acting Flt Lt C T White 46972 Technical Branch included in the Gazette dated 2 June 1943. His family believe this may be linked to action at RAF Bone. Was there a published Despatch regarding the invasion of North West Africa - I cannot find one on the Hyperwar site.

Charles