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I have an Enfield #4 Long Branch 1944 that has been rearsenal. When I bought it 5 or so years ago it tried some Prvi 180 gr. Had 1 foot size 10 shot groups at 100 yds. Tried the Prvi 150 gr., groups now like 3-4 inches. I buy all of it I can find when I see it.
I would try a different bullet grain and see how it works.
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I just de Bubba'd a long branch. It came with a milled adjustable sight. With sierra 150 grain pro hunters its less than 2 moa at 100. Not bad for something that needed new wood all around. I got real lucky finding a used set from a great guy on falfiles. Free!
OP check out your front sight. There is an off chance I can send you a front sight. I have two British front sights marked zero. They ran from -30 to +75. About six or seven heights made. When I did my recent de Bubba I bought a three pack of sights from Apex that were supposed to be varied heights but they jack wagons sent me three of the same height. They are nice folks but don't seem to get things right half the time.
Anyways if you have a negative marked sight I can get you a little closer. For really knowledgeable Enfield part suppliers Springfield Sporters is very good. They have premium prices but they deliver.
ETA I recently read an post I stumbled across while searching for No4mk1 sight info. A Brit poster explained what a convoluted system they went through on sight zeroing. After ww2 during refurbishment many rifles couldn't be zeroed with the then available sight heights. One unauthorized move was to use the taller sight from a Sten IIRC. Since that was unauthorized they made up new sight bases with different heights so They could be zeroed with the standard height sights. (A silly endeavor when making sights was much cheaper).
You might heck your sight base for markings. I think 2 marked were in that later base
http://forums.gunboards.com/#/topics/178189
l found what read. Skip my comments and read the link.