Quite a bit on these triggers has been posted in various threads and in formal articles like the many by Peter Laidler.
EVERY part of the system has to be in good condition; not "modified, distorted, wobbly, etc before you can assess further.
The mounting of the trigger on the trigger-guard is a bit of a nuisance, but not insurmountable.
The "full bent" (front face of the cocking piece) must be perfectly flat and at the correct angle. If someone has "polished" it and made the face more "vertical" or even past vertical to a reverse angle, the trigger pull will be horrendous. There is no coming back if this has happened; for two reasons The hardened skin of the steel at this point is relatively thin; grinding it the wrong way, then grinding it again to correct that and you have just altered the vital interaction between the cocking-piece, bolt body and the safety catch.
The two "bumps" on the front face of the top half of the trigger must NOT be modified apart from the removal of a couple of microns of surface coating so that there is no odd "drag" as the trigger acts on the lower arm of the sear. And, there is more.
If you do not have a Lee-Enfield-savvy gunsmith within reasonable distance, check around here. I suspect that I live on the wrong side of the planet to pop over for a look one afternoon.
Be careful if you go shopping for "spare" parts. The only way to go is with new, previously-unfitted parts. Otherwise you may be chasing your tail because the pre-loved bits from scrapped rifles may also be worn (or "bubba-ed") beyond tolerances.