I would just add to this that para. G. (i) above seems to suggest stoning the face of the cocking piece while it is still on the bolt, which is practically impossible. You'll have to remove it from the firing pin first. For that you'll need to buy or make the simple two prong tool to remove the firing pin. Unscrew the bolt head and look inside and you'll see the two notches the two prongs or pegs on the tool engage with. You can make a nice one out of a suitably sized screw driver.
If the face of the cocking piece is grooved, rough, not at right angles to the firing pin etc., you'll need to reshape/resurface it. You'll need a very good hand and eye to do that manually. Otherwise get it ground. Any sharpening shop should be able to do that for you if you show them what you need.
If the angles look good and it is just rough or grooved, I would lap it on a diamond lap by hand - if you have the 'feel' to be confident you can keep enough pressure on it to slide it back and forth across the plate, while not rocking it from side to side etc AT ALL.
You can clean up the surface of the sear as well the same way: roll it as you pull it along the lap to maintain the curvature of the tip, then flip it over and roll again. Each side you are effectively completing a 90 roll and and together you get the 180 degrees of the tip, more or less.
Ensure the cocking piece does not wobble AT ALL on the firing pin. If it does, centerpunch the end of the pin to enlarge it and thereby tighten it in the threads of the cocking piece.
You could also lap the face of the bolt head face after you remove the extractor if you feel confident. While you're at it, you might want to get some headspace gauges and check the HS.
You can also check the squareness of the bolt face to the chamber by putting some layout bluing on the bolt head and seeing if it bears evenly against the gauge.
First talk to your old friend though and see if he tuned up the rifle already as he sounds like he knows what he's doing.
The reason you hear people slagging the accuracy of Enfields is mostly that they are abused and neglected and then expected to perform like something that just left the factory.
