Much to the disappointment of filmmakers and novelists, Elizabeth I and Mary Queen of Scots never actually met. Not that this has stopped them imagining the scene. Indeed, the moment when white-faced Bess sets eyes on flame-haired Mary is usually the centrepiece of the drama, the cog around which all the fictional wheels whirr.

Throughout her life, Elizabeth assiduously kept her cousin at such a distance she might have had the plague. It’s one reason I can’t abide fanciful rewritings of her story. But, as a new exhibition at the British Library shows, scriptwriters and novelists were not so far off the mark as I thought.

Elizabeth and Mary: Royal Cousins, Rival Queens, which runs until late February, is unusual in giving the queens equal billing. Even more exceptional are the long-lost items it displays, which cast a fresh light on this ever-gripping and, it seems, ever-evolving story.

Among its revelations is a letter from Elizabeth, written in 1584, in which she appears to consider releasing her cousin from captivity. It is an Indiana Jones discovery, the sort of gift from the vaults of which all historians dream. Mary’s biographer John Guy writes that: “I’d always suspected that a letter of this sort could turn up. Deep down, what Elizabeth really wanted was to settle with her cousin, as Mary did too.”

Had this reconciliation taken place, and the queens finally met, they would not have been in their prime but advanced middle age. By now, Mary had been a prisoner for 16 years, and was in poor health. Elizabeth was increasingly haggard.

Mary’s response to this momentous letter set out her terms: she would return to Scotland to rule jointly with her 18-year-old son James VI, promised to uphold the Protestant faith while remaining a Catholic, and would never plot against Elizabeth. She agreed also that James’s choice of bride would be vetted by her cousin.

It is breath-taking to think that Mary’s tragic end – one of the most famous executions ever known – was almost averted. Even at this late stage of her unhappy career she might have returned to Scotland and ended her days regally, rather than lose her head.

How different history might have been had she and James occupied the throne together, one a Protestant, the other Catholic. While their neighbours in Europe were in the throes of religious turmoil and ferment, Scotland could conceivably have become a model of toleration. It is even possible that, under his mother’s moderating influence, James’s fear of supernatural forces might have been curbed, and the country’s ferocious witch hunts avoided.

All this lies in the realm of speculation, which is enjoyable but ultimately pointless. Mary, it turns out, had no chance of being restored to Scotland and her throne. This was not because Elizabeth or her powerful advisers were in league against her (although many were), but because her own son refused to consider it.

James would do nothing to bring about Mary’s release. Brought up to despise and detest her, he refused outright to share the crown. In despair, his mother allowed herself to become embroiled in a plot to kill Elizabeth and put her on the throne. Her death sentence soon followed.

Among the revelatory exhibits in the British Library is a sonnet, thought to be among the last words Mary ever wrote. It was included with her farewell letter to her French brother-in-law, Henry III, written in the early hours of the day she died. Short and to the point, it shows she was not merely resigned to her fate, but eager for the end: “lacking health and heart and peace, There is nothing worthwhile that I can do; Ask only that my misery should cease”.

It is a mournful last wish. Yet the fact that, with the clock ticking, she turned to poetry makes it all the more puzzling that Mary left no personal account of her life. She was a natural writer, constantly in touch with friends, relatives and courts across Europe.

What we know about arguably the most famous Scot who ever lived comes mainly from her letters, court records, and the reports and memoirs of courtiers, ambassadors, assassins and spies. The closest thing we have to an autobiography are her recollections, taken down by her secretary, Claude Nau, while she was imprisoned. These are a valuable insight into how she saw some of the events that brought her downfall, but are patchy at best.

The recent discovery of these long-lost documents makes you wonder if more are to be found. After her beheading, were the queen’s rooms ransacked to remove evidence embarrassing or shaming to her captors? In her final months she was so fiercely guarded it is hard to imagine any secret diary or testament going undetected.

But it is equally difficult to believe that, in almost 19 years of confinement and intolerable boredom, she never once committed her private thoughts to the page. That she wove subversive messages into her embroidery is well documented. This urge to have her voice heard, even when behind bars, surely makes it possible, if not indeed probable, that at some point she also recorded her story.

If a diary or journal were ever found, it would be a historical Holy Grail. One of the reasons Mary is perennially fascinating is because she remains a mystery. There’s so much we would like to know. Did she have a hand in the murder of her husband Lord Darnley, or conveniently pretend to know nothing of what was planned?

Did her third husband, the Earl of Bothwell, rape her, as widely assumed, or was that the story put out to save her reputation? Did she hope one day to overturn the Reformation and restore Catholicism to her country? And what were her feelings on returning to Scotland, after her years in France, where they did things very differently – did she feel at home, or all at sea?

Perhaps most importantly of all, what sort of woman was she? Since the chances of discovering a fugitive diary are exceedingly slim, I suspect we will be searching for an answer to that crucial question for centuries to come.

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