There is a paper on the net, written in the early nineties, in which a US Navy Officer offers an analysis of the submarine and ASW operations in 1982. It is a bit flawed. I think that the author was called Harper.
1. He describes the British ASW effort as unsuccessful - yet neglects the point that sinking enemy submarines is secondary to stopping submarine attacks against your own forces. In that sense the British effort was 100% successful.
2. He lists the SSNs sent South as participants in ASW operations, but they were not due to worries about blue on blue situations, as noted in One Hundred Days by Woodward.
3. ASW was the Royal Navy's main role as part of NATO, which why we had the Invincible class to carry Sea Kings for constant ASW operations, and Sea Harriers to deal with the aircraft that provided the Soviet submarines with reconnaissance and over the horizon targettinkg for their missiles.
4. The Argentines planned to attack the supply lines down from Ascension with the ARA Santa Fe. The requisitioned vessels full of troops would have been particularly vulnerable, so any sighting of an Argentine submarine would result in attack,