To the manner born, as Hamlet said, and these were no two ordinary babies. He was born on June 25, 1900, and christened Louis Francis Albert Victor Nicholas – the Victor and Albert in tribute to his great-grandmother and godmother, Queen Victoria, and her husband Prince Albert of Saxe-Coburg and Gotha. Louis's mother Victoria, born in 1863, was the daughter of Queen Victoria's second daughter, Alice. His father, Prince Louis of Battenberg, born in 1854 in Austria, was the son of Prince Alexander and Princess Julie of Hesse, the oldest ruling Protestant dynasty in the world.

She, Edwina Cynthia Annette Ashley, entered the world on November 28, 1901, a descendant of the Native American princess Pocahontas, of the Prime Minister Lord Palmerston and of the reformer and philanthropist the seventh Earl of Shaftsbury. Her father, Wilfred Ashley, had been a colonel in the Grenadier Guards who became a Conservative Member of Parliament. Her maternal grandfather was a banker, Sir Ernest Cassell, financial adviser to King Edward VII and one of the richest men in the world. Edward VII was Edwina's godfather and she was named after him.

Silver spoons, then, of whom great things might be expected. When Mountbatten retired in 1965, he had served his country for more than 50 years in 35 different appointments, including over 20 years as a member of the Chiefs of Staff Committee, composed of the most senior military personnel in the British Armed Forces. He was a British Royal Navy officer and statesman, an uncle of Prince Philip, Duke of Edinburgh, a second cousin once removed of Queen Elizabeth II and mentor of Prince Charles.

During the Second World War, Mountbatten was Supreme Allied Commander, South East Asia Command, 1943-46, and he was the last Viceroy of India when it gained independence in 1947 and the first Governor-General of independent India (1947-48). From 1954 to 1959 he was First Sea Lord, as had been his father some 40 years earlier. Next, he served as Chief of the Defence Staff until 1965, making him the longest-serving professional head of the British Armed Forces.

On retirement he was associated with 179 organisations, from the Admiralty Dramatic Society to the Zoological Society. By any standards it was a remarkable life and his entry in "Who's Who" is second in length only to Winston Churchill's, partly because every minor organisation is mentioned. Asked once how he would like to be described, he replied: "Naval officer who became First Sea Lord after being Supreme Allied Commander and Viceroy of India and thus the best-known figure the Navy has produced since Nelson, as well as being the President of the Society of Genealogists."

The description, Lownie comments, "reveals much – Mountbatten's achievements, what he valued and his pomposity".

Lord Louis, who was always known from an early age as Dicky or Dickie, cut a dashing figure in uniform and Edwina was hailed as "the most beautiful woman in England" and "the richest girl in the world" with the inheritance from her grandfather. So when they married in 12th-century St Margaret's, Westminster, on July 18, 1922 it attracted attention around the world and was the society wedding of the decade. Members of the Royal Family attended including Queen Mary, Queen Alexandra and the then Prince of Wales – the future Edward VIII – and the crowd outside was estimated at 8000.

The marriage had brought together two of the most glamorous figures of the period but behind closed doors things proved to be far from perfect, with he once admitting: "Edwina and I spent all our married lives getting into other people's beds."

A stunning but highly strung socialite, Edwina was promiscuous and uninhibited about sex. She had at least 18 lovers including Indian Prime Minister Jawaharlal Nehru and a black singer and pianist Leslie "Hutch" Hutchinson. One story surrounding Edwina and Hutchinson was that they were once inextricably locked in a sexual position when she suffered from vaginismus – a condition that makes the vagina clamp around the penis – and the couple had to be taken in flagrante delicto by ambulance to be separated in hospital.

BBC producer Bobby Jay recalled: "I was at a grand party. Edwina interrupted Hutch playing the piano. She kissed his neck, and led him by the hand behind the closed doors of the dining room. There was a shriek and, a few minutes later, she returned, straightening her clothes. Hutch seemed elated, and before he returned to the piano, told me that, with one thrust, he had flashed her the length of the dining-room table."

Mountbatten was "devastated" by her infidelity in the early days of their marriage but, realising he had little choice in the matter, began taking lovers of his own, too. Lownie's book has photos of many of Edwina's conquests, including polo player "Laddie" Sandford, 7th Earl of Sefton Hugh Molyneux, Hollywood actor Larry Gray ex-cavalry officer Michael Wardell, negroid actor Paul Robeson, Hungarian Count Anthony Szapary, Guards officer "Bunny" Phillips, conductor Malcolm Sargent and Bill Paley, the founder of CBS and one of her wartime lovers.

There are photos too of Mountbatten's lover at South East Asia Command, Janey Lindsay, and his long-term mistress Yola Lettelier, supposedly the inspiration for "Gigi", the 1958 film about a precocious, carefree French courtesan.

Much as all these affairs make for titillating reading, Lownie's book is well above being a salacious romp through the bedrooms. In fact, he tells, the 38-year marriage – she died in 1960 aged 58 in Borneo after an arduous tour – while beset with infidelities, was a loving one where each discovered that they did need the other. Edwina's aimless pre-war socialite life of multiple lovers found new purpose during World War Two and afterwards when she performed much valuable humanitarian work.

Mountbatten at work was a mixture of charm and ruthlessness. He was said to prefer to accomplish his aims in an underhand way, even when the straightforward approach would have sufficed. He had his disasters, such as the infamous Dieppe Raid in 1942, when 900 of the 6000 Allied soldiers and commandos were killed, 586 were wounded and 2000 captured, with little gain. And did he act precipitously over Indian Partition, when hundreds of thousands died in the ensuing violence?

Wisely, Lownie holds back discussion of the rumours that surrounded Lord Louis – such as bisexuality, paedophilia – until after Mountbatten's assassination by the Irish Republican Army in 1979, rather than bringing the unproven accusations and gossip into his main text.

Lownie says: "Though both Dickie and Edwina have had individual official biographies many years ago, this is the first joint biography and is based on extensive research not just in their own private papers but also archive collections around the world, interviews with dozens of people who knew them closely and Freedom of Information requests on both sides of the Atlantic. What I found surprised me and gives a very different picture of the couple and ther relationship than in previous books."

The cast includes all the key figures of the Second World War from Churchill and Montgomery to Roosevelt and Eisenhower as well as the Duke of Windsor, George VI, the Queen, Prince Philip and Prince Charles, Charlie Chaplin, Noel Coward, Salvador Dali, George Gershwin, Joan Crawford, Fred Astaire, Barbara Cartland, Grace Kelly and Merle Oberon.

Everything a top-notch biography should be.

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