Michael -
Apologies for the necropost - I only just noticed this thread.
The FN Fal was introduced to British Military Service on or about 1954 as the "Rifle, 7.62 x 54mm, L1A1", and was more commonly known as the SLR, or Self Loading Rifle. Its' replacement, the Rifle, L85 (SA-80) began replacing the SLR and other weapons of the time (SLR, SMG, LMG) from around 1985 (hence the L85 designation). Full changeover from the SLR to the L85 was achieved by around 1994, once all TA units had finally been re-equipped.
My old unit was re-equipped in around 1993, if I recall correctly - I oversaw the process, as I was the Company Armoury Storesman at the time.