Looks like the "No1 MkV1" is actually a later restamp (probably by a civilian owner) as the original would have been a Crown with "Enfield" and date of production - the same as on an SMLE, but on the left butt socket. It seems that the data has been ground off, probably when it was rebuilt as a No4 Mk1.
Its not clear from the photos: does the rearsight use a spring-and-steel-ball like a No1 MkV, or has it been converted to standard No4 spring-and-plunger?
This the slightly later model - the 1933 No4 Mk1 Trials rifle. You can see the sort of markings they used on the butt socket.
Other side, showing the magazine cut-off (the reason why so many No4s have the cut-out in the forend).