As Christmas approached, the Observer found Rowan Williams, the right reverend, the Lord Williams of Oystermouth, former archbishop of Canterbury, primate of All England, and author of The Poems of Rowan Williams (Perpetua Press), relaxing at home in Cambridge, merrily extemporising Dogberry’s lines from Much Ado About Nothing in a passable rustic accent: “Though it be not written down, yet forget not that I am an ass.”

This, your reporter is bound to note, is not a side of this distinguished theologian that’s familiar to any but his inner circle. It turns out, however, to be authentic. Like several men and women of the cloth, Williams once nurtured an ambition to go on the stage, has preached on Macbeth and King Lear, and venerates Shakespeare.

If there’s one play that intersects at so many levels with the Church of England, it must be The Winter’s Tale. Happily renowned for its stage direction “Exit pursued by a bear”, it was first performed before the court in January 1611, the year in which the King James Version of the Bible was published. Ever since, Shakespeare and the Good Book have been informally linked as supreme expressions of the English language. Acknowledging the deep association of this play and the church, the former archbishop speaks passionately about The Winter’s Tale.

“It is,” he says, “one of the most linguistically dense, emotionally demanding and spiritually rich of all the plays.” He finds “a great deal of religious symbolism” running through a story of reconciliation that culminates in a secular resurrection with the coming to life of Hermione’s statue. King Leontes’s “O, she’s warm” is – for Williams – “one of the greatest lines Shakespeare ever wrote”.

Williams freely admits to the youthful temptations of the stage and to “a fleeting ambition” to be an actor. “I come back to Lear compulsively,” he says, and recalls that “of all unlikely things, I once played Dogberry”. Having rehearsed some favourite lines, he adds: “With all due humility, that was casting against type. I usually got the authority roles, such as Theseus [in A Midsummer Night’s Dream].”

Did he find Shakespeare any guide to being archbishop? “There’s plenty in Shakespeare,” he replies, “about the gulf between the robes and the reality. That’s helpful. And also the sense of paying attention to words. I’m glad I’d done some acting: it’s a way of feeling the words. You’re playing a role, but that does not mean you are falsifying. It just means, ‘This is what I have to do to keep this community fulfilling its purpose’.

“One of the problems for the church today is we don’t know what we’re for.” Shakespeare, by contrast, was a master of the compelling presentation of complex themes. “I don’t happen to be Shakespeare.”

As archbishop, Williams struggled to articulate a version of his faith that would satisfy the irreconcilable factions of a worldwide church – die-hard evangelicals, crusading gay clergy and the determined advocates of women bishops – and still have relevance in the 21st century. He preserved unity, but at the price of theological gridlock.

A deep thinker, he was in an impossible situation. At times, the best he could offer was a retreat into meditation. At the contentious Lambeth conference of 2008, he reports that he “got all the bishops together in the cathedral for long periods of silence, on the principle that the building [Canterbury Cathedral] ought to be doing some work”.

His successor, with whom he speaks regularly, has proved more worldly and more successful, the natural church politician Williams never was. Some would say – Williams seems in his cryptic way to encourage this thought – that Welby is reaping a harvest of change sown by his predecessor.

Looking back at his time as archbishop and his frustrations over the ordination of women bishops, does he have regrets? He certainly seems to concede being conscious of a lost role and of a part given to another actor. “It’s odd,” he says, “when I see a photo of Justin [Welby]’s enthronement. I think, ‘Gosh, that’s the same scene, the same costumes and the same dramatic moment’.” This tradition stretches back to St Augustine. “But,” he says, with a slightly wistful expression, “now there’s a different person in the middle of it. The faces change, but Augustine’s seat doesn’t.” In retirement from the cut and thrust of church politics, which was never his forte, Williams is Master of Magdalene college, Cambridge. Now, with more than a hint of Prospero about him, he’s immersing himself in Shakespeare. In the approach to Twelfth Night, he will, with Salley Vickers and Stanley Wells, lead a four-day reading retreat on The Winter’s Tale, open to the public, at Cumberland Lodge in Windsor Great Park, Berkshire, from 2-5 January.

Williams says he is strongly drawn to this late “romance”, with its themes of reconciliation and renewal explored by a writer who, he observes, was intimately acquainted with conflict and jeopardy.

“Shakespeare loves living dangerously, doesn’t he?” he says with relish. “Look at Macbeth. A new play for a new king [James I] which speaks directly to his paranoia about witchcraft. Here’s Shakespeare, standing on a knife edge. He’s writing a play about James’s ancestors. And what does he do? He puts in this shameless bit of dynastic propaganda where he says, ‘Look, there’s Banquo’s line’, and it culminates in the best king [James] since sliced bread. You can almost see him turning to his patron, beaming and bowing, before getting on with the rest of the play.”

William Shakespeare has been an inspiration to the archbishop throughout his life. Photograph: Getty Images

The archbishop breaks off. For a moment I wonder if he is going to search out some matching biblical reference. “It reminds me,” he says, with a rush of secular excitement, “of a moment in The Simpsons, an episode about the press. Mr Burns is talking about the evils of newspaper proprietors when he turns to the camera and says, ‘Except for Rupert Murdoch’, and then carries on with the scene.”

Speaking of jeopardy, there’s an old debate about whether Shakespeare was a secret Roman Catholic. Williams has views on this. “Shakespeare knows exactly where he does, and doesn’t, want to go, in matters of church and state. He deliberately puts some of his plays right outside the Christian, Tudor/Jacobean framework. For instance, King Lear takes place in a pre-Christian Britain. Again, some people argue that Cymbeline is about a rupture with Rome, leading to a reconciliation. I think Shakespeare did have a recusant Catholic background. My own hunch is that he didn’t go to church much.”

Williams briefly recalls his meetings with popes John Paul and Benedict, “a very shy man”, and then starts to muse again on the character of our national poet. “He’s always ‘Sweet William’. As if he’s the chap you like to have around, but not necessarily the life and soul of the party.”

The archbishop’s fascination with Shakespeare has recently taken tangible literary shape in what he nervously calls “a bit of imaginative writing”. He confides that this is a short play, entitled Shakeshaft, in which he reconstructs a dialogue between the young poet and the great Jesuit theologian Edmund Campion. “We know they both stayed at the same house in Lancashire,” he says. “I found this a wonderful idea to play with: what might a Jesuit martyr and Shakespeare have said to each other?”

The perils of former church politics are vivid in his mind, which may help explain his reluctance to be drawn on the great issues of his tenure, especially same-sex marriage and the ordination of women bishops.

The conversation swerves into the fate of Thomas Becket, hacked to death by four knights on the steps of Canterbury cathedral in 1170. Williams admits that he can’t help identifying with Becket.

“You can’t not be aware of previous archbishops,” he says. “Every year we’d commemorate Becket’s martyrdom. We’d have prayers and readings, and I’d stand there, thinking …” His voice tails off. “Inhabiting that history was extraordinary. I found it one of the most intense moments of the year, a reconnection. We would read from Murder in the Cathedral and actually open the door of the north cloister, as Becket had done. I would listen to the bolts being drawn and think: those bolts … that door ... this stone …” An addict of meaningful silence, Williams hardly needs to add the chilling words of the chronicler of that act of high clerical murder, “the crown of his head was separated from the head in such a way that the blood, white with the brain, and the brain no less red from the blood, dyed the floor of the cathedral”.

In more secular times, but at the end of an equally dark year, does he have a message? Williams frames an ironic smile. “A Christmas cracker?” A pause. “Well, one of the great legacies of our culture is that we have a supremely great poet who keeps reminding us how words make us who we are. This means that having good words around us – an imaginative context that feeds us – is not a luxury but a necessity of life.” Another pregnant pause. “The amazing thing about our language and imagination is that we can never say, ‘We’ve done that’. There is no last telling.”

In the absence of scripture, could he teach his faith from Shakespeare? Williams considers the idea carefully. “I’d have a jolly good try.” He smiles enigmatically, before reprising his role as Dogberry.