Cutting to the quick Shooting master, your rifle is a bog standard, run of the mill, everyday No4T. It left H&H without a telescope. We know this because the butt isn't marked with the telescope number. The chest is really irrelevant because they weren't fitted into chests at H&H, that was done at Weedon where they all went.
At the end of the war, on the termination of contract, H&H were required to complete the contracts as best they could with the material in hand. In other words, they could not charge anything else to the Ministry of Supply who issued the contract on behalf of the War Office. So incomplete rifles, like yours and even half completed stock were returned, as-is! The rifle is put into a chest at Weedon and marked 'less telescope' because it hasn't got one. When Weedon closed in 1959 or so and the Small Arms were sent to Bicester, someone there fitted a telescope from a scrap rifle 52222 or whatever it was.
As I said, they are my thoughts is this rifle/chest was waiting next to my bench to be inspected and repaired. The first thing I'd note was the telescope number that was all akimbo and get that sorted out. Test it on the 28 foot collimation chart, bore sight and get the paperwork numbers corrected