There were some suggestions that the British had deployed a nuclear missile submarine to the South Atlantic to deter the Junta, or even to make a demonstrative attack in the event of the loss of a capital ships - though most of these reports were made following the war. For example, the New Statesman carried a number of reports on the topic in 1984, though these were of dubious provenance. They were based mainly on conversations between a Conservative MP and the Labour MP Tam Dalyell, and in the words of Lawrence Freedman, "may just have been a mischievous test of the latter’s gullibility". There is little official evidence for Britain considering the use of nuclear weapons against the Argentine Mainland during the Falklands War. A number of ships that were part of the Task Force were carrying tactical nuclear weapons as they were heading south - Brilliant, Broadsword and the two carriers were carrying nuclear depth charges, while other ships were carrying associated materiel. The weapons were taken south mainly due to logistical concerns, though there were also some worries from the RN about the risk of intervention by Soviet submarines. As the campaign progressed, the possibility arose that the ships carrying the weapons could be lost to air attack; this would be a major problem. As a result, it was decided to offload the weapons onto ships heading back to the UK. This was done for the weapons aboard Invincible on the 28th May, though those aboard Hermes could not be removed until the 26th June. There were also suggestions in the media at the time that these weapons might be used. The German paper Der Speigel reported that tactical nuclear weapons were being carried by the Task Force, and that Admiral Woodward had permission to use them in the event of heavy air attacks - though this was a speculative article, especially since nuclear depth charges are not a good anti-aircraft weapon.

Britain had issued what was called a 'Negative Security Assurance' in June 1978, as part of a United Nations Special Session on Disarmament. This assurance included an undertaking not to use nuclear weapons against non-nuclear nations, even if attacked, unless said attack took place in collaboration with a nuclear nation. While Argentina, which had not signed the nuclear non-proliferation treaty, was not technically a non-nuclear state, British use of nuclear weapons would not be following the spirit of the assurance. Britain had also signed and ratified the 1967 Treaty of Tlatelolco. The treaty established Latin America and the surrounding waters, including the Falkland Islands, as a nuclear weapon free zone. Not every Latin American state had signed or ratified the treaty, including Argentina (which had signed, but not ratified it), but it provided an extra assurance that Britain would not use nuclear weapons against Argentina. Finally, the British government, when questioned about their possible use, denied that it would use them. On the 27th April, Viscount Trenchard would state ‘categorically that there is no question at all of our using nuclear weapons in this dispute' during a discussion in the House of Lords.

Follow on question: aren’t the Exocet “codes” a myth?

Edit. I used this be in the navy in an occupation that dealt with anti-ship missile defence and I’ve never heard of Exocet codes. This makes me suspect that codes refers to something else, like how the missile seeker operates

**edited to add i have seen the term Exocet codes when reading about the falklands war, but I have never heard that term used in a military professional / technical sense.