Basically the L1A1 and the FAL is the same rifle. But there are a number of differences, the breech block had gooves cut into it to dispel dirt and crud, the rear sight, cocking handle, front sight, the gas regualator, the gas plug, the pistol grip, the flash hider and magazine were all different. If memory serves me correctly the firing pin was also different. However, both the FAL and the L1A1 were used more or less in exactly the same way.
The main difference is, the FAL was manufactured using metric measurements, while the L1A1 was manufactured using imperial.
Another weapon which was used during the Falklands to good effect, was the BREN gun, rechambered for 7.62 NATO.
When I was TA in the Queens Regiment, Charlie G gunners were issued the Sterling for self defence. I dont know if this was the case with the Para's or the Royal Marines.
I remember reading about either a Para or a Royal Marine picked up an Argentine FAL, was horrified at its dirty and overall poor condition. He stated that the Argentines obviously hadnt mastered the art of using a cleaning kit.