Who was the key ally for the UK during the Falklands war?
Well, as the British campaign employed no allies, the question fails immediately.
However, if the question asks which nation offered the most assistance , then it can be answered.
Many people will say the Americans, and yes, their intelligence was valuable. However, anything the Americans provided always came at a cost (think of the fuel so many Americans think they provided at Ascension Island, fuel that was bought and paid for so not free) so while assistance was offered, it was not given without expectations of something in return.
A country that offered the use of its naval bases was Chile, but as it was in a permenant Cold War with Argentina, such an offer again would have provided Chile much prestige on the international stage, so the offer was not given freely.
Many people will point to the Gurkhas. These marvellous warriors are supreme soldiers and we are blessed to have them serving amongst our forces. However, they are not a country, they are soldiers from Nepal, and India and Singapore also have Gurkhas serving in their forces, so as per the question, the Gurkha regiments may be thanked but not their country. By extension, the Chinese laundry workers on board the ships and members of other countries in the civilian fleet, did not represent their countries, so none of them are the answer.
In my mind, there is only one answer. New Zealand.
New Zealand was the only country from my memory, that offered to fight alongside the British and while their generous offer was gratefully declined, they went on to supply their own warships to take over from Royal Navy ships in other areas of the world. This was done not out of expectation, or world prestige, it was done out of generosity from one Commonwealth country to another. At the end of the conflict, once Royal Navy ships were freed to resume their original roles, the New Zealand warships returned to their own original duties.
No fanfare, no press conferences, just a resumption of routine once again.
New Zealand is my answer, and I thank them as a British woman and partner to a Falklands Royal Marine veteran. Thank you New Zealand.
example:
HMNZS Canterbury (F421), relieved HMS Amazon in 1982