I'd have thought Elint and radio intercept via satellite was probably more useful. (If you read the recent book about the sinking of the Belgrano it's apparent that somebody was reading the Argentine orders - make your own mind up about how that was being done
FWIW Former Labour Foreign Affairs minister Edward (Ted) Rowlands MP (now Baron Rowlands), in a debate in Parliament on the Falklands War on 3 April 1982 revealed that we (the British) were reading Argentine diplomatic codes. Rowlands was criticised for revealing this intelligence source, as the likely result of his disclosure was that the Argentinians would secure their systems and the intelligence would dry up. Mrs Thatcher called it "utterly devastating".
As Labour MP for Merthyr Tydfil, Rowlands was an experienced former Foreign Office minister in the Labour government who was involved in earlier Falklands negotiations in the late 1970's
He remained a Labour MP and from 1987 onwards served on the Foreign Affairs Select Committee. His "reading the codes" disclosure obviously had no effect on his future prospects as he was appointed a CBE in 2002, and in June 2004 he was given a life peerage, as Baron Rowlands of Merthyr Tydfil and of Rhymney.
As Hansard reported on Rowlands' participation in the debate on 3 April 1982:
Secondly, I have great difficulty in understanding how the intelligence failed. Our intelligence in Argentina was extremely good. That is why we took action in 1977. We found out that certain attitudes and approaches were being formed. I cannot believe that the quality of our intelligence has changed. Last night the Secretary of State for Defence asked "How can we read the mind of the enemy?" I shall make a disclosure. As well as trying to read the mind of the enemy, we have been reading its telegrams for many years. I am sure that many sources are available to the Government, and I do not understand how they failed to anticipate some of the dangers that suddenly loomed on the horizon.