Exulting in El Alamein, the first great British victory of the second world war (and the only one without the assistance of US forces), Winston Churchill told the House of Commons on 11 November 1942: "By a marvellous system of camouflage, complete tactical surprise was achieved in the desert." This quote, and what lay behind it, is the subject of Rick Stroud's The Phantom Army of Alamein. It does not appear in Jonathan Dimbleby's account of the same battle, and indeed the entire subject of Stroud's book occupies a single, uninformative paragraph in Destiny in the Desert (Profile, £25). Seventy years on from Alamein, it is obvious that no consensus exists on what really counted in a clash that everyone at least agrees was pivotal.

Operation Bertram at El Alamein was the largest visual deception campaign in history. It involved an elaborate shuffling of real and dummy forces, with hundreds of tanks and artillery moved overnight into combat positions hidden under canvas covers that disguised them as harmless lorries, and leaving decoys behind where the tanks and guns had been. German reconnaissance would report that nothing had changed overnight. They would also report a large build-up of forces in the south, all dummies. The dramatis personae behind this operation and earlier subterfuges  such as the building of a dummy railhead in the desert from palm fronds and old petrol cans  make up Stroud's subject. The cast of camoufleurs includes the stage magician Jasper Maskelyne; the leading expert on camouflage in the natural world, Hugh Cott; and assorted artists under the leadership of the documentary film-maker Geoffrey Barkas. With this group, in particular Barkas and the artist Steven Sykes, Stroud celebrates some unsung heroes of the second world war. Overcoming prejudice from the fighting forces, institutional inertia and a chronic lack of resources, they nevertheless achieved what many thought impossible: hiding armies in the desert.

That the colourful tales told by Stroud should be entirely missing from Dimbleby's account is odd. He does, however, attempt to correct some misconceptions that have hardened into myth and to rehabilitate some reputations that have suffered. One such sidelined figure is Field Marshal Archibald Wavell, a restrained, scholarly soldier and a lover of poetry (his anthology Other Men's Flowers was published in 1944 and is still in print). Wavell and the flamboyant, irascible Churchill never got on, and Wavell was dismissed on 21 June 1941. But, in seeking to rescue Wavell's reputation, Dimbleby misses one of his most important contributions to the later battle.

On 23 April 1941, Wavell had drafted a memo to the camoufleurs with a one-liner that would prove the key to the deceptive operation: "Is it a wild idea that a tank could be camouflaged to look like a lorry from air by light canvas screens over top?" The memo is preserved in the National Archives and reproduced in facsimile in Stroud's book. The idea was realised in the camouflage workshops in the desert, and the disguised tanks became known as Sunshields. The idea was also adapted for field guns under the name Cannibals. Seven hundred and twenty-two Sunshields, 360 Cannibals, 500 dummy tanks, 150 dummy guns, and 2,000 dummy transport vehicles were used in the campaign.

In the end, the important question is: was the great camouflage deception at Alamein an important factor in the victory  as Churchill, Montgomery and the camoufleurs believed  or not? Useful testimony comes from General von Thoma, commander of Rommel's Afrika Korps, who was captured on the last day and dined with Montgomery as his guest that night. "He is a very nice chap and he was quite willing to talk about past events," Montgomery wrote in his diary. Von Thoma confirmed that the Germans were fooled by Bertram: they expected the attack to come from the south and were completely taken aback by the ferocious assault from the north.

But what Churchill omitted to say in his report to parliament  and Dimbleby makes clear  was that following the initial surprise attack, the British advance became bogged down in a minefield. In the end the battle was one of attrition, and the larger British force prevailed (Dimbleby stresses that the empire and Commonwealth component of this force was considerable, with large Indian, Australian, New Zealand and South African contingents).

As far as the actual combat goes, the stories told by Stroud and Dimbleby tally, and similar quotes and anecdotes appear in both books. But Dimbleby has the fighting, the broad diplomatic picture sans camouflage, and Stroud the fighting plus lashings of camouflage. Dimbleby also has a personal connection that lends his narrative a passionate edge: his father was there, at least part of the time, as BBC war correspondent for two years until July 1942.

Dimbleby stresses Churchill's attempts to get his own way with his generals and the Americans. It is sobering to read the saga of incompetence and backbiting in the British camp that preceded Alamein, especially the catastrophic Greek campaign of early 1941, which resulted in ignominious withdrawal and huge losses of men and equipment from the Middle Eastern theatre. Destiny in the Desert is no sanitised contribution to our self-congratulatory anniversary culture: Dimbleby is extremely hard on the hero of the hour, Major-General Montgomery. There's no doubt that Montgomery made himself unlikeable on many occasions, but in this account the dice seem loaded against him.

Seventy years on, we realise that perspectives have shifted and we see the past differently. In a strange quirk of events, last year the RAF was bombing Benghazi once again. The scenario that prompted this return could not have been imagined in 1942. In September 2011, David Cameron visited Benghazi to praise the Libyan rebels, who had "fought like tigers". As Dimbleby stresses, in 1942 the wishes of those who lived in this region "were of no account to the principal protagonists".

So why was the first great British victory of the second world war being fought on north African soil at all? Because, as Dimbleby asserts from the outset, Churchill's war was as much to save the British empire as to save Britain itself, and for this he needed the help of an America that was always hostile to British imperialism. Churchill had to prove that the British could successfully engage the Germans in north Africa to enlist America in the goal of preserving British power in the Middle East. He succeeded in the nick of time. The victory at Alamein came four days before the first Americans arrived in north Africa for Operation Torch. Had Alamein been lost, the Americans would have had to do most of the work themselves and the British empire might have ended even sooner than it did. But for now, Churchill had the victory he craved.

 Peter Forbes's Dazzled and Deceived: Mimicry and Camouflage is published by Yale.

 This article was amended on 28 December 2012 to change the photograph. The original did not show Field Marshal Sir Archibald Wavell, but another distinguished soldier, Field Marshal Sir John Dill.