You might have thought that caricaturists and photographers wouldn’t share much in common, yet sitting down with two Glaswegian cartoonists, I quickly realise that they’re just the same — they all want the world to stand still.

“The worst thing is when you caricature someone and then you find they’ve got a new haircut,” moans Terry Anderson. “Or they used to wear glasses and they’ve gone and had eye surgery. Take Michelle McManus — after we drew her she lost all her weight! And Tony Roper, the comedy actor and playwright. He’s got this birthmark. Anyway, Chris [Somerville] draws him, takes the cartoon around for him to see, and he’s had it removed. It’s been there 50 years or whatever, and this year he chooses to get rid of it.”

For several years Anderson, Somerville and their four other colleagues at the Scottish Cartoon Art Studio have been working on more than 250 caricatures of well-known Scots. There are popular Scots, such as Billy Connolly and Robbie Coltrane; political Scots, such as Gordon Brown, Scotland’s First Minister Jack McConnell and the late Robin Cook; there are sporting Scots such as Sir Jackie Stewart and Colin Montgomerie; and a good few Scots that only those from north of the border would recognise.

Initially the project was intended to take the form of a book, entitled Fizzers, after the Glaswegian slang for faces. But when they were about halfway through they read an interview with James Holloway, the director of the Scottish National Portrait Gallery, who complained about the lack of contemporary faces in the gallery. “They have a lot of worthy, mutton-chopped industrialists, philosophers and so forth,” Anderson says. “But where’s the portrait of Sean Connery or Ewan McGregor?”

It so happened that they had already drawn most of the characters that Holloway thought should be there. At first the group was shy of approaching him, as the members were well used to the art establishment’s lack of interest in caricature, but Holloway was persuaded in an instant, and now more than 250 of the group’s “fizzers” are on show at the Edinburgh gallery.

It’s an extraordinary advance for the Cartoon Studio, as Somerville, now aged 28, set it up only seven years ago with a grant from the Prince’s Trust. It was a highly unusual venture as most caricaturists try to scrape by on their own. The British tradition of cartooning doesn’t make it easy either, as Anderson explains: “In France political cartooning and caricature are two separate disciplines, but over here they have coalesced. Think of Gerald Scarfe and Steve Bell — caricatures are highly politicised.”

In contrast to the cartoons of Scarfe and Bell, you can look at the portraits in Fizzers and have no idea what opinions the artists have of their subjects. Indeed, sometimes they didn’t have any opinion at all because they didn’t really know who they were — their subjects were chosen at random out of a hat.

Their goal is simply to convey a true likeness. “You could easily get a person to look familiar by putting them in the costume they’re famous for,” Somerville says, “but we want people to recognise the people without them. For instance, I drew Gregor Fisher, who is famous for being Rab C. Nesbitt. Nobody has seen Fisher without his hair all messed about, but I’ve drawn him as he really is.”

Anderson adds: “The humour in a caricature is actually something to do with the way our minds work. People tend to think they carry around a kind of filing cabinet full of photographs of the people they know, but that’s not the case. We actually carry an archetypal template face, and we recognise people by how much they diverge from that idealised face. The challenge for us as caricaturists is to play upon the differences that people already focus on. In a sense, we’re trying to make people look more like themselves by making them look less realistic. It’s a distillation.”

Initially, the group came up with 400 names and whittled them down. That still makes numbers tight, especially when they have included adopted Scots such as Magnus Magnusson (originally Icelandic), Jerry Sadowitz (born in America) and J. K. Rowling (a Gloucester girl who took Edinburgh to her heart). However, the other self-imposed limitation was that there must be photographic records of each subject. “We’re bound to the camera,” Anderson says, “so we haven’t done anyone who died before the advent of photography. Otherwise we’ve got to work from other artists’ paintings or sculptures, and they’re unreliable. The farthest back we go is Charles Rennie Mackintosh.

“It’s hard to say how long each one took,” he says, “because there’s the actual time it took to produce the final artwork, and then there’s the time it took to produce all the roughs. But the notorious one, the absolute gold standard, was Ewan McGregor — Derek Travers didn’t it get right until his forty-seventh attempt!” “He’s just such a pretty boy, you see!” laughs Somerville.

Fizzers: The Alternative National Portrait Gallery is at the Scottish National Portrait Gallery, Edinburgh (0131-624 6200), until July 2