Leafy, distinguished Merchiston, though too respectable to indulge in bed-hopping or, at any rate, to gossip about it, has become Edinburgh’s Bloomsbury, home to its most fashionable authors. It is where, behind walls high enough to keep out the muggles, J.K. Rowling lives. Not far away resides Ian Rankin, author of the Inspector Rebus novels, and two doors from him, Alexander McCall Smith. You can spot his house from all the scaffolding. It is being rebuilt — “knocked into one, actually” — by the profits of Botswana’s No. 1 Ladies’ Detective Agency.

“Oh, I have never met anyone who couldn’t do with another room,” says McCall Smith when I ask why, with both his daughters now at university, he needs more space. For a start, he explains, he needs to house all the foreign editions of his books. English language sales of his six No. 1 Ladies’ Detective Agency novels, starring the “traditionally built” Mma Precious Ramotswe, are approaching ten million but he has written more than 50 books and been translated into 34 languages.

The publisher’s statistics go on, but none is more sickening than that he writes, with little need to revise, at the galloping pace of 1,000 words an hour.

He offers me a cappuccino from the expensive machine that his royalties have also bought, but I opt for Mma Ramotswe’s preferred beverage, bush tea. “Now please feel free to say, ‘That’s interesting but I think, perhaps, I would prefer coffee’,” he says. But the tea is rather good and although I sip it genteelly from a china cup and saucer in a first-floor drawing room plashed by the wintry Scottish sun, I feel the better travelled for having sampled it. It is, I say, remarkable how many people he has made interested in the slow-moving life of a peaceable, relatively prosperous African country. Even 20 years ago Britain surely would have been too xenophobic, not to say racist, to care about Botswana.

“I think,” he says, “that one of the positive things which seems to have come from it, which I’m very happy about, is that people who previously might not have had the lives of people in somewhere like Botswana personalised, see that, my goodness me, these are straightforward, ordinary people — ‘people like us’ — leading lives with ordinary ambitions and hopes and fears.” Were McCall Smith a different sort of person he might scrutinise his background and ask if his rose-tinted presentation of Botswana does not compensate for imperial guilt. He enjoyed a privileged childhood in white-ruled Rhodesia, where his father, another Alexander, worked as a public prosecutor.

Like most of their tribe, his family had few personal relationships with the native population. Were he less honest, Sandy, as he is known, might even concoct a story about how, aged 18 and a student at Edinburgh University, he was shamed by Ian Smith’s fossilisation of Rhodesia as a racist state. But no, he says, it took him a long time, and probably not until he returned to teach law in Africa, to address the politics of his homeland. Even now it is rarely discussed in his novels.

“When I wrote the first of these books, I had no idea what I was doing.” He pauses to emit a high-pitched giggle. “What I mean was I didn’t have an agenda. I didn’t have any particular thing that I wanted to do. I did, however, want to get across a picture of one of these rather — actually, really, very fine — people whom I’d met when I worked in Botswana.” The inspiration for Mma Ramotswe (Mma is pronounced “murmar” and means madam) was a woman he spotted one day making clucking noises as she chased a chicken across a yard — “an image of Sisyphean labour, natural empathy and good humour”.

Her fictional consequence is an unlikely heroine for our cynical times and the pleasure of her acquaintance is only deepened by knowing that she has been invented by such an unlikely author. McCall Smith is not black, not female, not her age. He is an old-fangled 57-year-old who dresses, this morning at least, and possibly permanently, in a tweed jacket and Paisley tie. He has missed a patch of skin shaving and errant whiskers flare from the centre of his left cheek. The only passing similarity with his heroine is that he, like her, might benefit from losing a stone.

“Ten pounds,” he protests. I hasten to say that no one would call him “traditionally built”.

“Which is an expression I actually invented and now seems to have gone into the language. I think it’s in the latest Oxford Dictionary.” Readers, I say, will be horrified to learn that in the latest book, Blue Shoes and Happiness, Mma Ramotswe goes on a diet. She has, he says, aggrieved on her behalf, been feeling got at.

On less corporeal matters, McCall Smith resembles more closely his other lady detective, Isabel Dalhousie of the Sunday Philosophy Club series, a well-to-do Edinburgh spinster who edits The Review of Applied Ethics. Isabel does good not spontaneously, as Mma Ramotswe does, but through the application of ethical principles.

These latter, until he left his professorial post at Edinburgh University a few years ago, were McCall Smith’s professional calling. His 30 years in academia are gently parodied in his three Portuguese Irregular Verbs novellas but were serious enough to culminate in a stint chairing the Government’s Human Genetics Commission. We should not be surprised to notice that his entertainments are constructed on strong moral foundations.

“Novelists are doing a bit of anthropology and a bit of sociology and a bit of philosophy,” he says. “I don’t think of myself as a crime novelist but I do think that the crime novel is very concerned with moral issues. Auden wrote about the attraction of the rectification of the moral scales that you see operating in the crime novel.”