There were some striking "things behind bolt" issues with the L1A1 rifle. If the hammer isn't being pushed back far enough, it might not catch the sear reliably. The test would be live round followed by dummy round, what happens when you pull the trigger on the dummy round, does it click.I had a H style buffer pad installed and it is beat to schit. I wonder if that also contributed to it?
a worn out firing pin gives you no-fire, not double taps. However a sticking firing pin (corroded, bent, etc) can cause problems. Take it apart. That pin is supposed to float. If it isn't floating very freely, then you have identified your problem.