Your trigger may need "tuning" and/or you may need a bit of practice to get used to it. I don't think it coincidence that Lee Enfields, P14 Enfields, M1917 Enfields, Boer, Spanish '93's and Swede '96 Mausers and German, Belgian and Czech 98 Mausers all had two stage triggers, and safeties that engaged the cocking piece separately from the trigger sear. When set up properly - polished, perfectly square surfaces, straight and lubed pins in snug fitting holes, it is a system that works well, tolerates a lot of dirt and abuse, and is my preference, especially with nearly frozen or gloved fingers during our winter hunting. Many higher end target rifles are set up with two stage triggers, albeit with somewhat lighter pull weights than the military rifles.
When properly set up, you should have a "lighter" first stage pull - say 2 1/2 pounds or so - you should feel trigger movement up to a definite "stop". With a bit more weight to break through that stop - say 4 or 5 pounds - the rifle should fire with very minimal movement at that second stage. I have seen many attempts to convert to single stage - by grinding on the trigger "humps". Very few conversions are actually improvements, in my opinion - they all end up with really minimum sear engagement, to reduce felt trigger movement. They may exist, but I do not recall ever seeing an after market trigger for a Lee Enfield that your Parker Hale is built from.
A Parker Hale sporter 303 is a $250 hunting rifle, not a $3,000 bench rest target rifle. Bench rest guys do not walk around with cartridges in the chamber, often do not even have a safety, and have entirely different trigger set-up needs than a hunter.
