It’s gloves off in Shakespeare land. In the red corner is Stanley Wells, the eminent scholar who champions the “Cobbe” portrait of William Shakespeare (thin face, long nose, knowing look), lately proposed as the only one the playwright actually sat for. (It goes on show in Stratford next month.) And in the blue corner is a retired Bell Communications engineer from Canada, Lloyd Sullivan, who champions the “Sanders” (red hair, enigmatic smile) as the only portrait the playwright actually sat for.

Sullivan is a man with a mission, and the story of his lifelong quest has landed him in the company of the world’s leading Shakespeare scholars as the subject of a new documentary, Battle of Wills. It’s a mystery tale, and at its heart is the Sanders portrait, which has been in Sullivan’s family for generations. He first announced its credentials in 2002. The artist was an ancestor, a minor player in Shakespeare’s company had the same name, and the painting had a label on the back that claimed it was a likeness of a 39-year-old “Shakspere”, which was how the Bard spelt his name in his will. The Sanders family were also related to the Ardens, Shakespeare’s mother’s people. Sullivan’s claims were met with the plaudits and put-downs familiar to observers of this supercompetitive scholarly field.

The story gathered pace in 2006, when Sullivan went to Connecticut for an exhibition at the Yale Center for British Art called Searching for Shakespeare. The show, which originated in London, at the National Portrait Gallery, brought together a number of the contending portraits, including his own Sanders and the NPG’s Chandos portrait (domed forehead, looks like a bank manager). Among the show’s visitors in London was Alec Cobbe, a British art restorer. For both men, the show had the same impact. Each left, fired up. Cobbe had spotted a similarity with a family portrait. Sullivan, meanwhile, crucially needed to link his own roots with Shakespeare’s. He began a virtual search of the Midlands.

Sullivan found his inspiration in a self-trained historian in her early fifties, Pam Hinks, who lives in a modest house outside Worcester. On her sitting-room wall is a life-size reproduction of the Sanders portrait, which she affectionately calls “Old Smiler”.

She and Sullivan have never met. In fact, Sullivan, now 76, has never visited England. For the past five years, the two have communicated via thousands of e-mails and hundreds of phone calls, the tiny fragments of evidence going back and forth. Sullivan has sunk his life savings into proving the authenticity of the painting. Hinks, so gripped by his labour of love, has given her time for nothing.

“I got involved when Lloyd’s cousin found me on the internet,” she says, referring to the moment when Sullivan decided that he needed someone on the ground in Shakespeare country. “It’s a hobby — no, it’s an obsession, really,” she corrects herself. Knee deep in boxes, and with files often on the bed, she is clearly in her element.

Hinks has shared her maybes and hunches with her grandson and her late father in what Anne Henderson, the director of Battle of Wills, describes as “a giant family board game. They would all try to work on a part of the Sanders tree”. Now her husband, Tim, joins her on car journeys around the parishes of Worcestershire and beyond. She works discreetly, apart from the occasional moment when, she says, she can’t help herself: “I leapt up and punched the air in a records office once!” Her perseverance and gimlet eye have paid off; among her finds is a family will, including “eight pictures”, which raises the prospect that one might be the Sanders portrait.

Battle of Wills is full of nuggets of intrigue. One trail leads to Coughton, in Warwickshire, the heart of the 16th-century Catholic underground and linked with the gunpowder plot through the Throckmorton family. Their ancestral home had a secret chapel. Apparently, a Sanders attended Mass there. Shakespeare, some scholars believe, was Catholic. Of noble blood, his mother’s family, the Ardens, certainly were. The skeins come together: did the artist meet his sitter at the chapel?

Hinks’s smallest findings make their way back to Sullivan and to Daniel Fischlin, a leading Canadian Shakespeare scholar with whom he is writing a book. Fischlin rebuffs the Cobbe, producing scholarly and stylistic evidence for its sitter being Sir Thomas Overbury, a man imprisoned and poisoned by James I. From his Canadian vantage point, Fischlin suggests that the quest for authenticity says much about British national culture, the need to nail the image of Shakespeare.

That British sensibility inspired Henderson to focus her film on the Sanders story: “The fascination with this 400-year-old portrait is very modern. Because we live in the age of photography, we want to stare at the faces of our greatest artists, to learn the secrets of their inner life. We imagine a connection with the human being in the portrait, as if the person gazes back at us too.”

The London art dealer Angus Neill represents the Sanders portrait in Britain. In the film, he makes his argument against the Chandos, a portrait that is fast losing ground. He describes the Cobbe as “a highly polished and accomplished portrait of a nobleman, but completely lacking the ‘spiritual power’ of the Sanders, which I can only describe as the Mona Lisa of Elizabethan portraiture”. Neill’s love affair with the Sanders began when he saw the image as he flicked through a magazine while waiting for a train: “I nearly fainted. When I went to the NPG show, the Sanders knocked everything else off the wall.”

It is not only art specialists who have warmed to the Sanders, which Hinks suggests was painted to mark Shakespeare’s final stage appearance, for the King’s Men in 1603. The actor Joseph Fiennes, who played the Bard in Shakespeare in Love, features in Battle of Wills (as do Michael Pennington and Simon Callow), waxing lyrical about the feel and spirit of the smiling painting. Yet gut feelings do not authenticity make. Sullivan put the painting through a battery of tests at the Canadian Conservation Institute. The analysis was favourable, but not conclusive. And what of the long-faded label on the back?

“Shakspere

Born April 23 1564

Died April 23 1616

Age 52

This Likeness taken 1603

Age at that time 39 ys”

Analysis of the ink and paper suggests that the label is from the period, but counter-scholars argue for 100% proof. Sullivan is resolute, as he told me last week: “Our ancestor left us clues and verifications that his painting was, indeed, of the Bard. The most important clue is the label. . . no other painting in the world has a direct link to the sitter being Shakespeare attached to the painting itself.”

When Henderson set out to make what began as a modest art film, she offered to include the Cobbe. Its owner declined. His own claim now provides an unexpected prelude to Battle of Wills. For Sullivan, who lost his eldest daughter in the week the Cobbe was unveiled, it is a tough time to do battle. But he has his kindred spirit in Worcestershire. Hinks remains convinced that “Old Smiler” is the One. “His face says, ‘You’ll not find me out. . . ’ But I will,” she says.

Battle of Wills premieres at the 27th International Festival of Films on Art, in Montreal, on Tuesday; the Shakespeare Found exhibition, featuring the Cobbe portrait, is at the Shakespeare Birthplace Trust, in Stratford-upon-Avon, from April 23

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