I would not be surprised should you obtain wonderful accuracy with this rifle: Churchill of London knew their stuff.
I have a very similar rifle "made by" BSA and still sporting the original WW1 barrel and it is amazing. That particular rifle was a gift from my long-time shooting partner, shortly before he passed away and it is definitely the best-looking rifle I have. First time I shot it, it went 8 for 10 on the 300-yard 6-inch plates, rapid fire, using the 1960 Weaver steel-tube K-4 scope that came with it.
After War Two, England was in a terrible fix financially but they had heaps of guns. Many were surplused to the Trade, which modified stacks of them into sporters and sold them here in North America for hard Canadian and US dollars with which to back the pound Sterling as the British economy clawed its way back from bankruptcy to prosperity.
Your rifle has London Proof House markings (arm with scimitar), calibre designation, cartridge case length and operating pressure in Long Tons per square inch of pressure. A capital "R" on a part indicates that it was made by Remington at Ilion, New York, an "E" means that it was made by Remington at their Eddystone, Pennsylvania plant, and a "W" would indicate Winchester manufacture. No matter because they all interchanged and, by the time Churchill was finished, they would have been PERFECT. As with British law at that time, Churchill then would have marked this rifle with their OWN serial number.
My "BSA" rifle still has the original First World war barrel attached. You might be able to ascertain your Barrel Date by looking at the TOP of the Barrel, about 2 inches behind the Muzzle. There once was (and still could be) a US Ordnance "Flaming Bomb" with the date on installation of your barrel. In this case 10-18 will indicate October of 1918, 8-17 will indicate August of 1917 and so forth.
Your rifle looks to have 4-groove Mauser-style rifling, right-hand twist. Original military barrels had 5-groove Enfield rifling, Left-hand. This means that your barrel has been changed-out for a barrel from Churchill's own production. They were VERY good.
When these rifles were sold here in the late 1950s and early 1960s, they sold for $65 to $100 for the rifle, PLUS the scope..... and scopes were expensive back then. That does not sound like a lot, but I was working in a restaurant for 50 cents an hour and was happy to get into a bakery at 70 cents an hour, even if it meant starting at 5AM and walking to work in 35 below. The Dollar was MUCH bigger..... and you got a lot less of the things. This was an EXPENSIVE rifle and worth every penny. The reason they sold was that they were priced a little less than a Winchester Model 70 at the same time.
Somebody has worked on your rifle since it left Churchill's shop. That is what the clear (epoxy?) damping rest in the forestock is all about. Don't remove it; many of these rifles shot their best with a damping-point either right there or a little forward of that point.
VERY nice example of the British gunmaking Trade in the late 1950s/early 1960s..... and also of "what happened" to so many of those P-14s and P-17s to make original specimens so scarce today.
Personally, I don't think there is a production-class rifle made today to compare with these....... at least under about 4 grand a copy.
Love it and look after it: it's a Keeper for sure.