I've been meaning to do this for years and after seeing Gundoc's results I thought I'd get my finger out. The markings on the lid were splodged out in the typical fashion, first in thick white paint then again in black.
I know the rifle to be a former 3rd battalion Royal Green Jackets rifle as the UIN number is present on the chest, however imagine my surprise when all was revealed.
The EX PJW refers to a well known exercise called Pond Jump West which was carried out in Wainwright, Canada. I can only conclude the second battalion who at the time were just down the road from the third battalion in Warminster were preparing their L42's for the exercise on the range and suffered a break down and borrowed a rifle from the third battalion. The very nature of the markings make this in my view plausible as it wasn't at all common to mark the name of an exercise on a transit chest.