The rear "cradle cap" (isn't that a childhood disease? ;-) is a replacement.
File marks on the tube are obvious as Peter pointed out, sad but true. From those beveled screws on the "cover, segment, locking, cell, erector" or words to that effect, and the rough casting I would bet this was a KL scope, before it met the mill bastard, so to speak. The knurling on the drums is right for them, despite the lack of solder in the numbers.
The 1956 Faz barrel probably came from the same rifle that donated the trigger guard and sear. Could be one of those UF56 rifles that were sold by Parker Hale in the 1960s. Quite a few of them seem to have turned up out here. The sale mark is not normally seen on Mk2s AFAIK.
The Long Branch MkI cocking piece is worth a few bucks now.
Forend looks right and UKproduction(?) Handguards are LB obviously, the rear one at least.
The fitting of the pads looks a tad rougher than other trials "T"s with lower serial numbers: file marks on the top of the front pad, slightly off-center threaded hole in front pad.
The marks made by the shell mill cutter on the front pad are interesting. The mating surface on the front pad needs to have its edges carefully dressed to remove the burrs that have developed around the outside edge.
The edges of the receiver underneath look rougher and less well dressed than one normally sees on trials No4s also.
The setting pointer on the elevation drum is a nasty bodge compared to most others.
I can't be as sure as I thought I was in my previous post about the originality of one of the drums to the scope. Could be either way.