There aren't many options for scope mounts that don't mean drilling holes, which would be a pity after all that work and expense. S&K did make a no-drill mount for the No.1, but it still requires removing a bit of wood. They gave up making that mount though, probably because the top of the charger bridge on a No.1 is not flat enough or consistent enough in dimensions to make a stable base. Your most authentic option would be a repro of the base Parker Hale made for the No.1 during or after WWI which sat in the backsight base and was intended for the Winchester A5 scope. The next option would be a Weaver rail "scout" base that also fits in the backsight base and would mount a long eye relief scope; nothing "period" about that though!
Lots of info on your iron sight options here:
Service and TArget Rifle Sights ~ Parker-Hale and B.S.A.
Nice looking parts. Some careful whittling for the butt marking disc eh? That LSA receiver has probably seen plenty of action.
I see you got the barrel seated on the shoulder as well as the rear face of the barrel(?). Always a good thing IMHO.
The finish won't be to everyone's taste here, but you can always change that if you find someone who does a nice rust blue.