For the conservatives in the Church, Williams has always seemed dangerously liberal; for the liberals, he has often proved dismayingly conservative. For many outside the Church, his institution is an irrelevance anyway, with the gay marriage row underlining precisely why Church and state should be uncoupled. All this, in a 24-hour media age, where most of us are bored by non-downloadable forms of spirituality.

And yet, through all this “dim-witted prejudice”, as he has termed it, Williams has held his Church together. He has found common ground for homophobic Africans and touchy-feely Americans. He has brought solemnity to national occasions such as the royal wedding. He has debated willingly with evolutionary biologist Richard Dawkins and his atheist disciples, while sharply criticising Tony Blair’s wars and David Cameron’s austerity programme, with good grace and a subversive spirit.

When I meet him in his office at Lambeth Palace — light-filled and aching with books — he is far from the distant intellectual of popular legend. He is shrewd, eloquent, even upbeat, as if a weight has been lifted. Even if he describes the capital as “a deeply shadowed kind of city”, I sense he will be sorry to leave London. “There are wonderful strands of the positive in London,” he says. “I love walking along the South Bank. Something about the enormous cultural vitality generated by all those buildings …” (He and his wife Jane are regulars at the National Theatre.) “But walk 20 minutes southwards and you’re into some of the most conflicted and deprived communities that the capital has.”

He describes inequality as our most present evil. “How does London carry on being a city without being a conglomeration of walled settlements with ethnic and class distinctions entrenched?” he asks. “One is wary about localising the Devil, but [he is present] anywhere and everywhere that barriers are being reinforced between people. It would be nice to think that the Olympics could be experienced as that kind of positive challenge: can we actually make it feel like a city without walls, to use a good, biblical phrase?” I tell him I fear the VIP lanes for Olympic officials might run counter to his hope. “Well, ha ha.” His eyebrows dance a little, telling their own story. (It would be nice to think an honorary role could be found for them when their owner stands down.)

It is the more hands-on work he will miss, he says, especially in his parish in Lambeth. Williams is unusual in rising to become Archbishop from an academic career and, for a man prone to deep reflection, there is solace in practicality. “At the very basic level, religion is uncompromisingly committed to not ignoring people,” he says. “My faith is one which tells me everybody is worth whatever time, attention and love you can possibly give.”

Certainly, the role of the Church in post-riots London is not to be underestimated; in London’s most deprived boroughs, religion is often the strongest alternative influence to gang culture. Williams is eloquent on our misunderstood youth. “When young people gather together on a street corner, it doesn’t necessarily mean that they are a homicidal, drug-addled gang; they need one another’s company because they feel frightened too.” When he wrote as much in the past, he was rebuked for defending gang culture. “How very sad that we don’t want to see or hear what ordinary young people in cities are saying about themselves,” he says. “It’s so much easier to say they are frightening. We ignore them as far as possible, and when we can’t ignore them we try to batter them into submission.”

He is, as you would hope, the forgiving kind, but he does find it enervating quite how often his words are twisted. “That was one of the times when I felt really angry about the way the media had responded. Not so much because of myself — I’m getting rather inured to it — but because of the issue that vulnerable, not at all violent people were saying they were fed up with the way they were stereotyped.”

Does he feel that, sometimes, the misunderstanding has been wilful? (As when he seemed to call for Sharia Law?) “Not wilful. There are some things where I think the reaction was lazy and dishonest. One of the problems I’ve felt is that as an archbishop, you’re always talking to everybody. So if you are giving a lecture to an academic audience, it’s very easy to take a sentence out and say, Good grief! Intellectual gobbledegook! Well, I don’t necessarily talk like that when I’m preaching in Peckham.”

He smiles meaningfully when I suggest that he must be relieved to return to academia — “I shall to some extent relish being away from the daily spotlight” — though he may still make arts programmes as Master of Magdalene College, Cambridge. In his academic studies, he hopes to think about (slight sigh) “the nature of the excess of religious languages, the way it sometimes says more than it needs to”. He will also gather his writings on secularism, hopefully addressing the evangelical atheism that has grown in fervour in recent years.

“We are haunted by Christianity in this country; there’s a bit of can’t live with it, can’t live without it in some people’s approaches. Even with Dawkins, the sense that he can’t leave it alone is fascinating. It does mean that it’s a more complex phenomenon than it looks at first; it’s not as if everyone on that side wants to sweep things away and start from day one. I’m interested in how much scope that still gives for mutual understanding.”

I think we will come to miss Williams in national life. He functions in the exact opposite way to a politician, looking for mutual understanding, while embracing doubt. If there is a consistence to his inconsistency, it is to suggest that perhaps religion’s role is not to provide easy answers but to pose difficult questions; that complexity and paradox may be worth considering too. “That is hard in a short-term media age.”

Certainly, it’s hard to imagine any successor providing a Dostoevskian reading of the Leveson Inquiry (he once told David Cameron he should read more of the great Russian novelist). “Dostoevsky is an amazing analyst of cliché, of the half-thought, and the half-feeling of politics, Right and Left. But what Dostoevsky is pushing at us all the time is that you are responsible for a great deal more than you know. You are answerable for the people you want to ignore. That cuts both ways. You may find that the words you used innocently are actually responsible for pushing someone else into despair or violence.”

One thinks of all the protestations of innocence offered by former News International CEO Rebekah Brooks and Culture Secretary Jeremy Hunt, always believing that they were in the right. “Exactly,” he says. Does he think there’s a danger that the cynicism this inspires in people can also lead to a form of despair? “Hmm … that’s where the religious perspective comes in. The Dostoevskian picture of human beings says you have to look at yourself and realise just how much of a mess there is. You have to avoid liberal and conservative lies; you have to bring it all into the light; but the light is benign.”

I think he is telling the Government, the media, the police, the judiciary, to step into the light. What more could we have asked of a spiritual leader?