That s/n is from the period when info is sketchy. They made 253 guns from 1902 thru 1918.
The last gun made in 1901 was 3699 and the first gun made in 1918 was 3952.
It's unlikely they made many if any during WWl, so your date of 1914 is probably about right.
There were 3 Thos. Horsleys from York, the first founded the company in 1932. On his death in 1882,
his son took over until his death in 1915. The grandson of the founder, also Thomas (1869-1954), and three of his brothers
continued the business until it closed in 1959.
From the pics, no side clips, typically English rose and scroll on the receiver, and later stock extension.
Very nice gun. Personally I wouldn't lengthen the chambers, but the gun's value is as a superb field gun,
not as a collectible. Good luck with her!
My info came from:
https://www.amazon.com/British-Gunm...+gunmakers&qid=1618772142&sr=8-1