During the Second World War, a huge wallchart at the Admiralty, the Royal Navy’s London headquarters, starkly illustrated the dire straits in which Britain found itself. It showed the number of ships being sunk at sea at a time when 95 per cent of the nation’s fuel and 70 per cent of its food were being imported. If the rate of sinkings stayed below a red line near the top of the chart, Britain could survive on the supplies making it through on the convoy ships crossing the Atlantic. If the line were breached, the country would fall. At the start of 1942, the graph was nudging the red danger line. German U-boats operating in ‘wolfpacks’ were devastating the convoys. Only a handful of people knew how close Britain was to defeat.

Simon Parkin’s enthralling narrative history tells the story of the secret unit charged with turning the tide in the Battle of the Atlantic. Gilbert Roberts, an officer who had been invalided out of the navy with TB, was appointed to lead a team of Wrens – members of the Women’s Royal Naval Service – to work out using war-gaming techniques how the U-boats were so successful and develop tactics that would enable the convoys’ escort ships to avoid or sink them. Roberts was a talented strategist and an enthusiastic advocate of war-gaming. Although it was already used by the navy, there was scepticism about its efficacy. But desperate times called for desperate measures.

Wrens also excited considerable suspicion. There were heavy restrictions on the types of jobs they were allowed to do – their motto ‘Never at Sea’ had a deliberate double meaning. In peacetime these young women – some were only seventeen – would have been expected to marry and bear children as soon as possible. For many of them, this was their first taste of freedom. The Wrens assigned to Roberts had to be whip-smart, highly numerate and tactful enough to deal with some gargantuan male egos.

Roberts’s outfit, the Western Approaches Tactical Unit (WATU), set up shop at the top of a building in Liverpool and designed a war game scenario that incorporated all known data relating to the Battle of the Atlantic. The floor was used as a giant board – a kind of linoleum ocean – upon which models representing ships and U-boats were moved according to a complex set of rules aimed at mimicking what would happen in a real battle in the cauldron of the mid-Atlantic. One team played the part of escort commanders, the other the part of U-boat captains. Ingenious ways of restricting each team’s knowledge of the movements of the other were devised. This was the closest thing the Admiralty had to a virtual reality simulation, ‘an imperfect yet instructive mirror of reality’, as Parkin puts it.

Late one night, there was a breakthrough. Fuelled by coffee and corned beef sandwiches, Roberts, along with 21-year-old Jean Laidlaw and 19-year-old Janet Okell, used official reports to replay a recent action blow by blow again and again, until eventually they were able to deduce the enemy’s strategy and formulate counterattacks. Over the coming months, the fresh-faced Wrens taught grizzled naval officers the new tactics by having them play The Game, as the simulation became known. ‘Make your mistakes here and you won’t make them at sea,’ Roberts told them, and he was right. In the summer of 1942, convoy escort ships sank four times as many U-boats as in the month before. By the end of 1942, some two hundred officers per month were playing The Game. Philip Mountbatten was among them, as was the author Nicholas Monsarrat (a version of WATU appears in his novel The Cruel Sea). The ultimate vindication of the unit’s work came in 1943, in a pivotal seven-day battle in the North Atlantic that the Germans would come to know as ‘Die Katastrophe’.

Parkin is a journalist rather than an academic historian and has a keen eye for drama and colour. This is a pacey read with some wonderfully vivid set pieces. These include a scene in which Roberts’s caustically dismissive superior watches a demonstration of The Game, realises that the team really is on to something and immediately sends a message to Churchill, and another in which the admiral considered to be Britain’s greatest living submariner is dumbfounded to discover that the opponent who has defeated him five times in a row is not merely a woman but has never even been to sea, let alone set foot in a submarine.

After the war, none of the WATU Wrens received any official honours. Few spoke of their work, but they never forgot it. When she died in 2015 at the age of ninety-three, Mary Poole, who had once got into trouble for laughing when Churchill asked her if she was frightened, still had her Wren headdress at her bedside. Roberts was honoured in 1944 with a CBE (he took two Wrens to the Palace with him) but was disappointed that, as the years passed, WATU’s work was largely forgotten. It was a blow when a war-gaming scene was cut from the film adaptation of The Cruel Sea. How thrilled he and the Wrens would have been to know that Steven Spielberg has already snapped up the film rights to Parkin’s excellent book.