I am sure the British would have had enough resources to keep check on 4 airfields.
from what I have read, the task force knew of when a raid was on.
A clandestine operation to watch is very different from a shooting match. If the British didnt know a Argentine fighter was airborne then you have to ask who was running this show and why was he in charge.
An attack on an airfield was a decidedly dodgy affair with taking the war to the Argentine mainland and the possible loss of civialian life. War is a diplomatic nightmare and neutrals may have come off the fence if that happened.