The 13Cxxxx rifle is amongst certainly not a sniper rifle as Scouser (T) stated.
Look for a scope serial number on the top of the stock, just below the cocking piece. If that is not there, and the butt has the Holland & Holland wartime code of “S51” on the underside, then the rifle is almost certainly a (T. LESS TELESCOPE) variant. These rifles were partially converted and most appear to have then been put straight into storage “for the duration”. Later they were sold surplus, sometimes in a No.15 Mk.I transit chest with the added marking (T. LESS TELESCOPE) on the front of the chest. Most of these rifles are found in near mint condition. They are not common, but some estimates are that about 3,000 of these rifles, which had been selected for conversion to sniper equipment, were left unfinished. Why? I do not know for sure, but the Britishobviously made a decision to standardize, using BSA Shirley made rifles, rather than having H&H have to deal with variations that stemmed from receiving rifles made by several different manufacturers. I speculate that H&H lobbied for one consistent supplier. Some 1944-1945 BSA made rifles are also No.4 Mk. (T. LESS TELESCOPE), but that is because they were unfinished at the time the contact ended, or else they had been rejected.
Another sign to look for is a “T” marking, with serifs, on the left side of the body. Early conversions did not always have this marking and it has been reported that some had it added retroactively in service. Naturally one does not want to be fooled by such a marking that might have been added after the rifle left military service to increase the sale price.
Genuine Stevens-Savage sniper rifles are rare, usually in the very low serial number range. One comes across these unfinished conversions much more frequently. When the serial number is in the 13Cxxxx range, one is pretty much guaranteed that it is an unfinished conversion.
The (T. LESS TELESCOPE) rifles are the easiest to fake as sniper rifles, since much of the conversion work had already been done by H&H i.e. cheek rest added, battle sight removed and scope pads fitted. As a result the presence, or not, of a matching No.32 scope/bracket/No.8 scope case, scooe serial number on wrist of butt and possibly a “T” marking are all features that need to be examined very closely.
The Stevens-Savage sniper rifles were fitted with No.32 Mk. I scopes. If the rifle went through Factory Thorough Repair (F.T.R.) for example, it might well receive a newer model scope in which case the old scope number would be cancelled on the butt and a new scope number added. As well, the bracket would normally have the rifle serial number stamped into the left side. One could expect such a rifle to have been well used. If it had new wood fitted, that wood would not likely have all been Stevens-Savage wood, but rather could be from any of the suppliers. The front scope pad on a well used one would likely have several stake marks per front pad screw, indicating heavy usage. The Imperial War Museum has a Stevens-Savage L42A1, presumably with the L1A1 conversion of a No.32 Mk.3 scope. They could not tell me the serial number however as they had not bothered to record that when they catalogued the rifle! Also it was on display, so it was not easily accessible.
Popping on an orphaned scope and bracket makes it look just like a sniper rifle, which is great if the set-up is cheap, but that does not mean that it ever was a real sniper rifle. Spending a lot of money on this would not be recommended unless the rifle was carefully examined and vetted by a very knowledgeable person such as Roger Payne.