The Rifle No. 1 Mk V and Rifle No. 1 Mk VI have peep sights. The former is basically a No. I Mk. III with a peep sight. The latter is pretty much the same as the No. 4, but the No. 4 as adopted has a heavier receiver and a different stock.
Roadkill, I think there is some confusion. There was no Rifle No. I Mk II or Rifle No. 1 Mk IV. The SMLE Mk II and Mk IV rifles were conversions of the earlier rifles and were never given the "Rifle No. 1" designation.
There is a Rifle No. 4, which is the WWII era rifle with a peep sight. The Rifle No. 4 Mk II is post-war and differs from the Rifle No. 4 Mk I only in having the trigger attached to the receiver instead of to the trigger guard.
Jim