Rather more than 20 ships served in the South Atlantic:
Hermes, Invincible, Fearless, Intrepid, Bristol, Sheffield, Coventry, Glasgow, Cardiff, Exeter, Glamorgan, Antrim, Brilliant, Broadsword, Active, Alacrity, Ardent, Antelope, Arrow, Avenger, Ambuscade, Andromeda, Penelope, Minerva, Argonaut, Yarmouth, Plymouth
Plus: Leeds Castle, Dumbarton Castle, Endurance, Hecla, Herald, Hydra
Plus subs: Conqueror, Courageous, Oynx, Valiant, Spartan, Splendid
Plus 22 RFA landing / support ships
Aside from a dozen or so Leander Class ASW frigates and a handful of aged Country Class Destroyers, I don't think there was an awful lot left in the tank, really - especially given NATO (and other) commitments and when Sir Sandy Woodward's memoirs suggest that the only real effective surface combatants he had were the Type 22s and 42s.