There is a lot of information about this complex operation. But can anybody explain why they chose to use an aircraft? They could easily shoot cruise missiles from a ship or ballistic missiles from a nuclear submarine. The easiest and quickest option would be just to shoot an ICBM directly from the UK using a conventional warhead. Just put the coordinates in and task done. No risk to anyone! I think the UK had all the needed technology by that time.
Because all of Britain's adversaries were either nearby (Warsaw Pact) or too far to economically fight (China). Since Britain's weapons only needed to reach the Caucasus, they simply never developed ultra-long-range assets like the Tu-95 Bear or B-52 Stratofortress. Unfortunately no-one was willing to provide any of those under Lend-Lease.
Honestly, even if the British had appropriate cruise missiles (they did not), they would have no reason to own ones with the range to hit the Falklands from Ascension. Nor would they have any reason to need ICBMs with the range to hit Falklands from the UK (they wouldn't have ICBMs in Ascension, who would they nuke? The Congo? Guyana?) Again the enemy is in Europe, so everything is sized and positioned to go just that far.
Your question takes for granted the pre-existence of weapons systems like the "down a chimney" Tomahawk. Honestly, the British inability to do anything but have their SSN crews shake their fists at the islands, was a major impetus in developing those new families of weapons. Every major force watched with keen interest and thought "Gosh, what if we had to deal with one of these?"
However, they certainly did have relevant weapons: Aircraft carriers. This type of mission is the reason carriers exist. They could project power from the Spratleys to, indeed, the Falklands.
Further, there'd be little point to using cruise missiles or ICBMs before the main force was in position to make good on the advantage. And once the main force was in place, they could strike from there, and did not need long-range weapons.
This is borderline as an aviation question but I will answer it anyway.
They didn't use those weapons because they did not have them at the time:
Conventional cruise missiles did exist but most were nuclear, and the UK didn't possess any conventional ones.
ICBMs with conventional warheads did not and probably still do not exist because they are not a good idea:
- Their capacity is low: A sub launched ICBM has somewhere around 2.5 to 3 metric tons' throw weight, much of that would be taken up by warhead guidance, thermal protection and other necessities so your actual warhead would be maybe 1000kg, or 2200lb. That's not that big a conventional bomb, and it could only launch one. A fighter bomber could drop 2 of those. The Vulcan bombers on the raid carried 21 1000 pound bombs.
- They aren't accurate enough: a nuclear weapon can be a bit off and still destroy its target utterly, a conventional weapon needs a great deal of precision. The Polaris missile had an accuracy of 3000ft (900m). That's okay for a nuke, it' still ruin someone's day, but completely inadequate for a 2000lb bomb. More modern ICMBs have more like a 100 meter accuracy, which is a lot closer but still not good enough for a conventional bomb
- They are expensive: that's a lot of cash for a 2000lb bomb that probably will miss
- Launching one could start WW3: If you launch an ICBM someone is going to see it and if they think it might be directed at them a retaliatory strike could be the answer. The world has come perilously close to this more than once, it simply isn't worth the risk!
The UK needed a surgical strike to neutralize the Port Stanley airport in the Falklands so that Argentine airplanes based there couldn't attack the coming UK convoy or the impending UK ground attack.
An attack by carrier airplanes wouldn't work because the carriers, and the accompanying task force, would also be in range of the Argentine planes based in Port Stanley.
Using nukes against the airport at Port Stanley would have destroyed Port Stanley and all the UK citizens there.
This hasn't been explicitly said, so: The UK didn't have cruise missiles or ICBMs with conventional warheads at the time.
The Trident II D5, the UK's only ever ICBM, entered service in 1994: BBC.
As for cruise missiles, the BGM-109 Tomahawk has been introduced in 1983 (US) and 1998 (UK): Royal Navy.
Someone mentioned the harrier wasn't able to carry a bomb heavy enough to crater the runway. The Vulcan's dropped 21x1000lb bombs on the Falklands. The Harriers in the Falklands dropped 1000lb paveways (Laser guided). They could carry 2 normally perhaps even up to 4. So they could and did drop the same size of bomb, probably more accurately. Though there was radar controlled guns and SAM that would have been made it very hazadous for low flying aircraft. Though the harriers did raid the airport on occasion.
Some of have suggested there was inter service political rivalry. The Vulcan raid was a another means for the RAF to contribute to the war. Though the Harrier GR3 pilots were RAF.
It was probably a combination of a lot of these factors.
As noted in a comment, the UK did have access to the UGM-27 Polaris submarine launched nuclear missile.
Launching a missile from a sub ranged a few hundred miles (or even a few thousand miles) off-shore would have been significantly less risky to UK military personnel and equipment. However...
Launching nuclear warheads against a target that you intend to occupy, as opposed to completely annihilate and make uninhabitable for a century or two (or three), is somewhat counter-productive. It also tends to, um, raise eyebrows in the international community.
Since Hiroshima and Nagasaki, no nuclear weapons have been used against actual foreign targets or people. Doing so would have been absolute political suicide for Thatcher and company, and would have most likely brought extreme backlash and sanctions against the UK as a whole.
Oh, and don't forget the numerous UK citizens who were actually living in the Falklands would have just been killed by their own government.
Because they could (just barely)
There is universal consensus that Black Buck served no military purpose. It did not impede Argentinian military efforts in any significant way.
Its purpose was not to be useful though. It was primarily to make troops there feel that the UK was supporting them. It was a morale-boosting exercise, nothing more (or less).
It did also have a second purpose too, which was to serve notice on the Argentinians that mainland Argentina was vulnerable to nuclear attack by Vulcan bomber.
Which renders the question moot. Whether or not the UK had any alternative abilities, it wouldn't have mattered because bombing Argentinian positions effectively was never the real goal.