I would take the suggestions here to heart. try several bullet weights and see which works best and hunt deer with that.
I own a bubba'd P14 of Winchester manufacture, 1916 Vintage. It has a Boyd's Laminate stock, Timney trigger and a 6x36 Leupold on top. It shoots the 150's and 180's with equal accuracy, and it is quite accurate for a 90 year old rifle. It will shoot the 150 Hornady and the 180 Sierra under 1" for 3 at 100 yards. I load the 150 Hornady with 48.5 grains of Vihtavuori N540, and the 180 with 51.0 grains of W760, they go 2840 and 2605 respectively. [These loads should not be tried in a Lee-Enfield, BTW.] Additionally, I purchased some of Steve Redgwell's 200 grain Mark 9 bullets (sized to .313, groove diameter of my P14). With a good load of Higginson 47N, it also shoots very well indeed. So I believe a decent barrel will shoot most weights well, but may show a preference for a given bullet, since they are made in several different diameters. I must be lucky, because the 3 bullets that shoot best in my rifle are all different diameters. [.313 - 200 gr.Mk 9; .312 - Hornady 150; .311 - Sierra 180] That being said, no bullet I have tried has shot over 1.6" in this rifle, and that includes the Speer 180RN, the Hornady 174RN, the Winchester 180 Powerpoint, the Sierra 150 Spitzer, and even some pulled military FMJ's in 174 grain weight. It is my "truck" gun, but I intend to shoot something with it this fall, since it seems totally dependable. Regards, Eagleye