I've come to really like the BSA International  for bench rest shooting. The rifle is set up with Unertl bases and the Unertl scope was fine, until I discovered the Nightforce scope.
I decided to make a Picatinny rail base for the BSA to use the Nightforce scope. Before making any chips, I did a search for BSA International Mark 2 information and discovered many helpful sites. 
I have several questions that users of this rifle might be able to answer and would appreciate any additional information.

My forearm is different than the standard Mark 2 and includes the two extra barrel fittings shown in photo #1. I think that the built in front rest is a BSA option. The two barrel fittings are professionally installed but I don't see them listed as a BSA option.

Does anyone know the history of these fittings?
Does anyone know how the front fitting is properly adjusted?

In researching the Mark 2, I came across the scope mount shown in photo 2. 
This looks like a better solution than making a Picatinny quarter rib for the barrel.

Does anyone know if this scope mount is still available?

Thanks,
Otto

There's still at least 1 Brit and 1 Oz. guy making those cantilever scope mounts - Check rimfirecentral.com, the Martini forum.  I have 1 of those too, but doesn't work for prone with my Weaver T36.
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One of the forum members from Australia offered the scope mount and ammo block for sale some time back. I am not sure if he is still offering them.

Thanks for the replies to my questions regarding the Martini's forearm and scope base.
FB
I agree that the distal fitting looks like a barrel tuning device. 
Do you know how it's adjusted? 
Is there any data that shows that it helps accuracy?
MB
Thanks for the rimfire central link. 
The scope bases were available in 2024. Hopefully they are still available but if not they don't look hard to make.
Otto

Are barrel tuners of that nature allowed for use in ASSRA competition?

My MkI International doesn't have one. Anybody know if they were a factory option, and if so were they offered for on the earliest iteration the MkI?

Waterman
Is your scope base fastened to the action or to the barrel. I'd expect that the barrel type might have more flex than the shorter action type. Attached are photos of the two types.
If I make a scope mount, I'll attach it to the action using the dovetail screw holes and extend it to also attach to the rear Unertl base screw holes.
I've been told by a member of our shooting club that he feels that the barrel tuner isn't helpful for increased accuracy. He is an excellent shot and I value his opinion.
There are a variety of barrel tuners and he may be referring only to the one on my rifle.
Do any of you who use barrel tuners of any type, feel that they significantly increase the accuracy of your rifle?
Thanks,
Otto

never owned a tuner, but in an "almost the same" thing, I have seen two rifles, a Winchester and a Browning with the gizmo they marketed to adjust for specific loads each improve quite noticeably by complete removal of the ugly thing. I would give your friend's advice some credence.  Just my opinion though.

The second device is a ammo holder block. It attaches to the right side of the receiver with the large headed trigger assembly screw. It is a nice addition when shooting in a timed march. Ammo is right beside the action opening and very quick for reloading.