Did the Admiralty take the threat of the Argentine Aircraft Carrier seriously? Could that old carrier have done any damage to the British Task Force, or even have sunk the British Fleet? I'm curious if there was any real possibility that ARA Veinticinco de Mayo would not have retreated, but instead pressed an attack on the Task Force.
Yes, the Veinticinco de Mayo was a threat to the Task Force during the RN had to consider during planning for the Falklands War. It was a threat for three key reasons, all related to its mobility. The Veintcinco de Mayo had an airgroup consisting of A-4 Skyhawk attack aircraft, and S-2 Tracker patrol aircraft. The Skyhawks were probably the most effective attack aircraft available to the Argentines - over the course of the war, they would sink four British ships, and damage seven more. However, they were comparatively short-ranged, able to reach the Falklands and strike only with aerial refuelling. The Argentinian Air Force had only two tankers, both KC-130 Hercules aircraft. This lack of aerial refuelling assets meant that strikes were limited to at most six aircraft. The 25 de Mayo gave the Argentinians the ability to launch strikes from well within A-4 range of the Task Force. This meant that the only limit on the size of strikes was the number of aircraft available aboard the carrier, giving the Argentinians a better chance to overwhelm the RN's air defences. Secondly, the British had no airborne early warning capability. To compensate for this, they deployed ships as radar pickets. These sat closer to the Argentinian airbases, extending British radar ranges to the west, and providing early warning of air raids. However, they could only do this because they knew where the Argentinian aircraft were coming from - there was only one threat axis. Veinticinco de Mayo provided another threat axis. To provide early warning against threats from her, another radar picket would have to be placed along this, diluting the Task Force's air defence. Finally, 25 de Mayo extended the range of Argentinian air strikes to the north and east. This was a threat, not to the Task Force, but to the sea lanes it relied on. The Task Force, operating far from British bases, was supplied by tankers and stores ships travelling from Ascension Island. These were safe from most Argentinian attack aircraft, with only C-130 patrol aircraft capable of reaching the routes they travelled. 25 De Mayo provided a way for the Argentinians to make strikes against this vital lifeline.
As with the General Belgrano, the Veinticinco de Mayo was, while old, a threat the RN could not ignore. The British response to the threat posed by both ships was similar - submarines were dispatched to shadow the ships, and sink them if necessary. Belgrano was shadowed, and ultimately sunk, by HMS Conqueror. The sub assigned to shadow 25 de Mayo was the new nuclear submarine, Splendid. She successfully located 25 de Mayo, but was unable to move into position to make a successful attack before 25 de Mayo withdrew. It is not entirely clear whether Splendid's captain had permission to sink Veinticinco de Mayo - but it is clear that this permission would have been granted had Veinticinco de Mayo launched a strike against the Task Force. HMS Spartan was also deployed to hunt for 25 de Mayo - while at times she was closer than Splendid, she failed to locate 25 de Mayo. The other major limitation on the threat posed by Veinticinco de Mayo was her unreliability. She had been laid down nearly 40 years before the war, and had been poorly maintained in Argentinian service. Her ageing engines limited her speed, meaning that heavily laden aircraft couldn't take off without strong winds across her deck. If these winds weren't available, as they weren't when she tried to launch a strike on the 2nd May, then she would be unable to launch, making her useless.