I have owned several No4Mk1's over the years and currently have an original condition 1943 vintage BSA made No4 that I got a few years back for $325. At the time I felt I was paying all the money for it, but I liked the fact that it hadn't been overhauled and the bore was in near perfect condition.
The very first centerfire rifle I ever bought was a No4Mk1 that I got sometime in the mid/late 60's. It was in like new condition and I believe I paid something like $25 for it. Of course the first thing I did was remove all the extra stuff from it that I didn't need for hunting deer. I later sold it and put the money towards a Winchester Model 70.
The .303 round is no slouch and it would drop a deer like it was hit with a hammer if I did my job and placed my shot properly.
I don't see a FTR stamp on it so I am going to go out on a limb and say that it was made at Fazakerly. From the condition it certainly has seen it's share of use over the years, but I personally like the been there-done that look. British military arms have a rich history due to their world-wide empire and conflicts on many continents spanning hundreds of years.
Now that you have WWII covered with your No4, you should be on the lookout for a No1 to represent WWI. Then of course, you should get a Martini-Henry for the pre WWI colonial period as well as a Snider.
Yes indeed, the rabbit hole is deep and expensive. I have a rather modest little collection of British rifles and am always looking for the next acquision.