The rifle in question is/was a No.4 Mk1 or Mk2. Without being able to look closer I can't tell the difference. However the No.4 Mk2 had the variation where the trigger assembly was fixed to the receiver frame and not, as in the Mk1, fixed to the wood.
The bottom wood has been shortened and reshaped.
The top 2 woods.
Middle and front bands (to hold the wood pieces)
It seems that someone has had an attempt to sporterise it. The sights are the "Battle sights" and flip-up/down for 100 yards or 300 yards. The finer "Singer" sights will fit.
From what I can see it would be relatively easy to bring back to Military spec.
Noticed that the rifle is cocked, I presume it has been cocked for the picture.
We are what we are because of what we were: