But then, as Parker is the first to point out, despite the quaintness of the company's headquarters in Street, with its old shoe-making machinery and Twenties posters, times are changing - and so is Clarks. The past year has been a revolutionary one for the company, the largest family- owned firm in Britain after Littlewoods, whose foot-measuring machines rank alongside Blue Peter and Enid Blyton as symbols of our childhood memories.
A keen flautist, Parker, 43, is the man who has been driving the changes. In the three years since he joined Clarks, he has moved most of the company's production overseas, shedding 2,150 jobs in this country. It is a strategy that has paid off. Earlier this month, the company announced a 7.9 per cent increase in operating profit, before items, to pounds 42.5m, the best in the company history.
Parker bursts out laughing when I remark that he doesn't look like a businessman. "The idea that business people have to wear a pin stripe and a tie to be effective is a rather outdated one," he suggests "We are becoming a more casual society and if you are running a casual shoe business like this, you don't want to be walking round in a starched shirt."
Under Parker's guidance, Clarks has set about shedding its stuffy image. The transformation received a welcome boost when Liam and Noel Gallagher of the pop group, Oasis, adopted Clark's classic desert boots as their own fashion accessory. The company's Wallabees range has also been rediscovered by the young and trendy, especially in Japan.
Parker also oversaw the highly successful "Act your shoe size, not your age" advertising campaign that's been instrumental in luring customers back into the stores. When Parker arrived, the fitted children's business - famous for its metal machines that measure shoe widths - was also "a bit in the doldrums", despite its market share of around 28 per cent.
"We were selling a fitted shoe but we weren't selling the nicest-looking shoes. Parents are demanding a nicer product for their children. There has been a huge explosion in kids fashion," says Parker. Clarks shoes now come in a range of trendy colours and styles.
The son of an army officer and former Desert Rat, Parker spent most of his childhood abroad. His first job after leaving Oxford University, where he studied Philosophy, Politics and Economics, was as an economist with The Treasury.
"I quite liked that, but after going up the steps every day for two years I realised that it might not make a career."
The salary, he says, was especially unappealing. So Parker took up a place at the London Business School to study for an MBA. His lucky break came when he met an executive at Thorn EMI. "He was an ex-Navy guy, and he believed in giving young men their first command," says Parker. "I half jokingly lobbied to be given the job of a small Chicago-based engineering subsidiary."
He got the job: so, at the tender age of 26, he started to run his first company. It was, says Parker "a dream job; people don't generally leave business school to go and run a business". He came back to England to run another company in commercial kitchen equipment and then, at age 30, was given the job of running Kenwood, then still part of Thorn EMI. During his time as head of the world's most famous food mixer firm, Parker quickly increased the business's turnover from pounds 53m pounds to pounds 200m. In 1989, he oversaw a management buyout and then spearheaded its flotation in 1992.
Parker, who has a Belgian wife and four young children and admits to being "a bit of a Belgophile", was headhunted for Clarks in 1995. "I wasn't that interested at first. Then I found out the company was turning over pounds 700m a year and employing 16,000 people around the world. I thought: 'Crikey, it's a really big opportunity.'"
The firm Parker joined was starting to turn the corner after an abortive take-over attempt in 1993 by Berisford. The bid had caused a bitter row between the family shareholders, some of whom supported it.
At the time, Clarks - which also has the K and Ravel brands - was also the largest shoe maker in the country, though its retail operations accounted for half its turnover.
"I said we can't be a wholesaler and a retailer and a manufacturer," explained Parker. "We've got to say: 'We are going to be good retailers of shoes, and that's where all our capital is tied up and that's where we need to earn a return.'" So he began closing factories across the UK and buying from abroad.
"Someone making shoes here gets paid pounds 15,000 a year; in Portugal they are paid just a third of that," says Parker. "There is no option. If you carry on making the shoes, your customers won't buy them because they cost too much."
Administrative staff, used to working in the protective environment of an old family firm, also felt the weight of Parker's axe."There were too many meetings and too much shared responsibility. I found I couldn't tie people down." About 400 admin jobs were also shed.
The next step for Clarks could be the company's flotation. When shareholders voted against the Berisford bid, they did so in return for a proposed float in 1998. That's obviously passed, but the issue is still on the agenda. Parker himself is in two minds about taking the company public. "We are not about to make a huge acquisition, so as a business we don't need to access new capital." He also sees the advantages of a family-owned firm.
"It's not like going to the City, talking to fund managers who just hold the shares professionally. These are real people who have a deep interest in the company because they have held their shares for a long time. The Quaker mentality is like holding shares for custodianship," says Parker.
"But in the long term, I see the company will probably want to look at where it can raise capital and that'll involve somehow injecting more equity," he adds.