Honestly if we're talking about the real world value of Vanguard, or any BBG as compared to a fleet carrier I don't think too many people would seriously argue for the battleship. That said, in terms of the Falklands I think you'd well and truly have to do something crazy to get a scenario in which Vanguard is available and some form of fleet carrier isn't; that is, of course, not nearly as true if the upgraded Tiger class ships are availabnle, but that almost happened OTL (and would certainly be in play if a second task force had to be launched).
I don't disagree that between a fleet carrier or a battleship I would take the carrier, but the point being argued here is that if Vanguard had been available to go help the Royal Marines take the Falklands back in April 1982, what would be the end result? That fact is pretty obvious, I would think - 800 15-inch rounds to toss at Argentine positions on one ammo load, which even if one doesn't consider the effect on Argentine morale would sure as hell inflict casualties.
As far as getting it there, I'd be inclined to go for the British-French union scenario during WWII. This brings the French Navy into the fight, preferably by them running from Toulon (shooting their way past the Italians if need be) to their new ports of call in England and Scotland, or perhaps if they aren't certain of safety going to Malta or even South Africa. This gives the RN a rather bigger set of units to use, and the French ships help the RN finish off the Italian Navy in 1943 and help with the battle against the U-boats in 1944 and 1945, followed by them being deployed in big numbers to the Pacific in 1945, starting with most of them being involved in shelling the crap out of Okinawa in April 1945. French army and air force units spend the war fighting right with the British, and after the war the idea of the Union staying together is very real. By the time George VI dies in 1952, the union is good and solid, and the idea of the two nations joined as one catches the wave of modernization in Europe.
Into this, Vanguard is the second to last battleship of the RN (The HMS Jean Bart, completed in 1949, is the last). The French ships all keep their names in the formally-unified nation but gain the British prefixes. The better economy of the 1950s unified state allows the battleships to be kept for a while, but all are retired from active service by 1958, and the older classes are all scrapped in the 1950s (with the exception of Warspite, King George V and Strasbourg, which all become museums in Liverpool, Portsmouth and Marseilles, respectively), leaving just the Jean Bart, Richelieu and Vanguard in the reserve fleet, where they remain. Despite the battleships helping with the fight in Algeria, Southeast Asia and Suez, they are widely seen as old and antiquated, though useful in certain situations - which is why they are not sent off to be cut up.
The change happens in Vietnam. Called back for service is USS New Jersey, and her turns on the Vietnam firing line are stellar, pounding the hell out of North Vietnamese positions. It is a surprise to the British and French, who in the midst of potential problems in their handful of overseas states suddenly are paying rather more attention to the three remaining battleships. Having been hurriedly completed and having a major flaw in only having a forward-firing ability, the Richelieus are dismissed from consideration and attention turns to Vanguard. Through the 1970s, the plans for the battleship kick around a number of times, but after the Turkish invasion of Cyprus in 1974 and the problems that come from that, the Royal Navy gathers its guts and calls Vanguard back to the colors in 1976, sending her to the shipyard where she had been built in Scotland for a major overhaul, but the yard's bankruptcy in 1977 in the middle of the refit sees the Vanguard do most of its refit at Chantiers de L'Atlantique in Saint-Nazaire, France. The rebuild is extensive - the 5.25" guns are replaced by modern 4.5" units in new double turrets, Four Sea Wolf missile systems, along with eight radar-directed 40mm Bofors guns, are fitted for anti-aircraft duties, while sixteen Exocet anti-ship missiles are also fitted in four launchers. Massive upgrades to electronics and amenities are also fitted, and the crew needed for the battleship falls from 1,975 to 1,260, and these sailors have much better amenities. Fitted and equipped as such, Vanguard raises the White Ensign again on June 16, 1980, 40 years to the day after the Union began, in Saint-Nazaire.
The battleship's first deployment is a round-the-world cruise, visiting numerous ports around the world, focusing first of all on the French overseas territories. Battery testing in Tahiti in January 1981 confirm the new fire control system for the ship works and works well, and for much of the first half of 1981 Vanguard rotates around the Pacific, based out of Hong Kong and visiting (among others) Tokyo, Manila, Sydney, Melbourne, Auckland, Fiji, Lima, Vancouver, Pearl Harbor, San Francisco and Los Angeles. She returns to the United Kingdom in August 1981, and has a good refit in England in the winter of 1981.
Upon the invasion of the Falklands in April 1982, Vanguard has been out of refit for mere weeks and was out on NATO exercises, complete with three Anglo-French fleet carriers, and on the order of the UK's government, all are organized into a single force to go get the Falklands back and set off to take the islands back. Vanguard, on account of its excellent flag facilities, is the ship on which the commander of the Task Force raises his flag, though the commanders move to HMS Hermes when the battle happens. The Royal Marines and French Marine Force are sent to take the islands back first, and the line is crossed when HMS
Rubis torpedoes cruiser ARA
General Belgrano on May 2 in the South Atlantic, and two days later HMS
Norfolk is struck by an Argentine Exocet missile and badly damaged, eventually sinking as a result. The day after that, the first Black Buck missions go off using Airbus A300 tankers and Handley-Page Victor bombers, doing critical damage to the airfield at Stanley and destroying several Argentine aircraft on the ground.
When the landings of the UK forces began on May 22, Vanguard was there to soften up the defenses. That night she fired her first shots in anger since Suez on the Argentines, doing a fair amount of damage to the Argentine defenses. The Argentine air force attacked Vanguard and cruisers Tiger, Blake and Colbert repeatedly, but while Blake took one glancing blow, Vanguard had a 1000-pound Argentine bomb detonate against her stern, destroying her Sea King helicopter and starting a substantial fire that was nonetheless put out quickly. Vanguard's AA defenses, however, claimed four definite Argentine kills and two probables, as well as providing copious amounts of gunfire support. The battleship and cruisers withdraw to re-arm on May 26, but are right back at it the next night. Colbert drops two Canberra bombers attempting to attack British forces on May 29, and
Tiger and
Colbert are hero ships on June 1, with the Bluff Cove air attacks being done with just the two cruisers and frigate
Jean de Vienne being all between the British landing ships and the attackers, and the ships did well.
Blake took a nasty hit amidships and
Jean de Vienne died defending the ships, but the forces managed to land despite damage to RFA
Sir Galahad and RFA
Sir Tristam. Blake's damage saw her withdraw, but she made it back home.
Vanguard was sent after this to directly shell the Argentine defensive line around Stanley, but the price of this was two Exocets fired at her, neither of which hit. Vanguard's gunfire landed a surprise when her gunfire wounded the Argentine commander in the islands on June 12, two days before the war was over.
Vanguard arrived back home on July 10, virtually out of 15" ammunition and having been damaged twice, but having without any doubt at all proven her utility in the modern Royal Navy. She was to have an active 1980s....
