HERE is the best book that has yet appeared on last year's Falklands war and a small gem of military and naval history reminiscent in many ways of Barbara Tuchman's The Guns of August. The authors have two stories to tell. The first is a brilliant narration of a short, violent clash in the freezing fogs and mountainous seas of the South Atlantic. The other is an informed analysis of the political decision-making that led to the conflict, raising those larger questions of war and peace which modern man approaches on bended knee.

The authors are two British journalists. Max Hastings' combat reports for the London Evening Standard are widely regarded in England as the best that came out of the war. An ex-paratrooper, he knows very well that bullets and high explosives kill, a fact that often seemed to surprise some of his less experienced colleagues. Simon Jenkins is the political editor of The Economist, a close observer of the behavior of politicians and diplomats in Westminster and Whitehall.

They do not attempt to show the war from the point of view of Argentina, and they do no more than sketch the problem of the Falkland Islands and their inhabitants in international law. What they do attempt, and very successfully, is a dissection of the most acute British military and political crisis since World War II. "We would like to think this book is more than instant journalism, if necessarily less than instant history," they write. "Let us call it an interim report on Britain's war . . . based overwhelmingly on the testimony of participants, at home and abroad, at sea and ashore."

From the first sentence, it is apparent that this is an eminently readable chronicle of "a freak of history, almost certainly the last colonial war that Britain will ever fight. So extraordinary an event was it that, even after men began to die, many of those taking part felt as if they had been swept away into fantasy, that the ships sinking around them had somehow escaped from a television screen into the living room."

Close students of military and naval operations will recognize in these pages, through the flash of gunfire and the smell of cordite, those indispensable accouterments of Britons at war: tradition and muddle. Thus, Prime Minister Thatcher is advised by a panoply of military and naval staffs and joint intelligence committees still in place 40 years after V-E Day as if Britain were a great world power with imperial responsibilities. Thus, the torpedoing of the General Belgrano was a perfectly predictable extension of hoary Royal Navy doctrine to go after an enemy's capital ships (Bismarck, Scharnhorst, the Kaiser's High Seas Fleet, etc.). Thus, H.M.S. Glamorgan can sweep out of the mist and shell Port Stanley proudly flying battle ensigns (exceptionally large, oversize flags) for all the world as if she were a ship-of-the-line at Trafalgar.

Thus, a British Admiralty can send a task force into enemy waters so woefully short of air cover and deficient in radar that many readers will ask whether the British admirals have ever really learned the lesson of the sinking of Prince of Wales and Repulse by Japanese aircraft off Malaya in 1941. Thus, 450 British paratroopers at Goose Green could attack what was thought to be an equal number of troops and to their own surpise defeat 2,000 entrenched Argentinians. Thus, Sir Galahad could lie off Fitzroy all day without disembarking its Welsh Guards contingent, an act of criminal stupidity not atoned for by the heroism of the rescuers after the ship was sunk.

Through the fog of war shines plenty of valor. Here is a unit of the elite SAS on a glacier on South Georgia: "On the first afternoon, three corporals probing crevasses advanced 500 metres in four to five hours . . . Their efforts to drag their sledges laden with 200 pounds of equipment apiece were frustrated by whiteouts that made all movement impossible. 'Luckily we were now close to an outcrop in the glacier, and were able to get into a crevasse out of the main blast of the wind . . .' They began to erect their tents. One was instantly torn from their hands by the wind, and swept away into the snow. The poles of the others snapped within seconds, but the men struggled beneath the fabric and kept it upright by flattening themselves against the walls. Every 45 minutes they took turns to crawl out and dig the snow away from the entrance, to avoid becoming totally buried. They were now facing katabatic winds of more than 100 m.p.h. By 11 a.m. . . . their physical condition was deteriorating rapidly. The SAS were obliged to report that their position was untenable, and ask to be withdrawn.

"The first (helicopter) to make an approach was suddenly hit by a whiteout. Its pilot lost all his horizons, fell out of the sky, attempted to pull up just short of the ground and smashed his tail rotor into the snow. The helicopter rolled over and lay wrecked. A second (helicopter) came in. With great difficulty, the crew of the crashed aircraft and all the SAS were embarked, at the cost of abandoning their equipment. Within seconds of takeoff another whiteout struck the (helicopter). This too crashed onto the glacier . . . .

"But an hour later . . . a miracle. In a brilliant feat of flying for which he later received a DSO, Lieutenant Commander Ian Stanley had brought another helicopter . . . down on the Fortuna Glacier. He found that every man from the crashed helicopters had survived. Grossly overloaded with 17 bodies, he piloted (the helicopter) . . . back to Antrim and threw it onto the pitching deck. His exhausted and desperately cold passengers were taken below to the wardroom and the emergencyymedical room."

The authors pay ample and unsentimental tribute to the seamanship of the Royal Navy, the dash of the Commandos and Paras, the stamina of the outnumbered Harrier pilots with their superb machines who flew as many as six sorties a day in all weather. Their discussion of a war fought with sea-skimming missiles is marred only by our curiosity for more detail. At the back of the whole operation looms the figure of Admiral Sir Henry Leach, the First Sea Lord clearly presented with the chance of a sea dog's lifetime, whose immense confidence about his service overwhelms cabinet doubts and sends the Royal Navy on a 8,000-mile chase to victory.

The authors seem scrupulous and fair in their assessment of the causes of the war. They convincingly show that if Argentine miscalculation of British resolve led to disaster, British diplomacy was also inept. After 17 years of negotiations, a solution was at hand by means of "leaseback," a device that would acknowledge Argentine sovereignty, yet preserve the rights and lifestyle of the islanders. But a "compromise settlement was never achieved because the British Foreign Office proved far more competent at negotiating with another government than with its own," they assert. "Successive cabinets regarded the political price of compromise always just too high. American diplomats take it for granted that an essential function of their job is to lobby politicians. . . . In Britain, the Foreign Office existed in a world of its own."

As with World War I, once the troops have marched and the ships sailed, their recall is unlikely. Had the Thatcher government not gone to war in the aftermath of the Argentine invasion, it would have been hurled from office. How a foreign war will preserve a party in power will disturb those Americans who ardently desire peace and disarmament. They may also ponder how cuts in defense spending would in time have made the British response impossible. For their part, the authors have no doubt of the legitimacy of Britain's cause. "It was a case of action by Britain or a victory for armed aggression over peaceful negotiation," they conclude. "It was an argument which the large majority of world states were ready to acknowledge throughout the conflict. It requires a strange ethic to maintain that the world is a less safe place now the crisis is over."