When you have somehow lured George Clooney into your sandwich shop, what do you do for an encore? Well, if you’re Josh Littlejohn, co-founder of Social Bite, a chain of five cafes in Scotland, you look down the list of other recent Oscar winners and invite Leonardo DiCaprio. News leaked in June that DiCaprio had accepted and he is due to arrive in Edinburgh next month as the guest speaker at the Scottish Business Awards, one of Littlejohn’s sidelines. Meanwhile, the very strange story of Social Bite, a social enterprise that employs homeless people and donates all its profits to charity, becomes ever more like a Hollywood movie script.

For Clooney’s visit to Social Bite, last November, crowds formed outside the Rose Street shop at 6am. By the time his car pulled up, there was hysteria. He swept in, took selfies with the staff, bought an avocado and pesto sandwich and donated £1,000.

“Yeah, it was mad,” laughs Littlejohn, who is 30. “And the next day, our little business – which three-and-a-half years earlier, I’d been serving behind that till – was on the front page of every newspaper in the entire country. It was on CNN, I had my cousins in South Africa saying, ‘Just heard you on the news.’ It must have been a slow news day. All that really happened was that George Clooney had a sandwich!”

There’s not too much A-list stardust at the winner of OFM’s Outstanding Achievement award on the morning I visit. A group of Edinburgh’s homeless linger outside: one in a hoodie and bobble hat puts down his can of Strongbow and goes in to collect a free sandwich and coffee. These meals are covered by customers who “pay forward” donations and Social Bite’s Christmas appeal. The handouts are supposed to be capped at one per day, but Littlejohn notes good-naturedly that often the same faces will turn up at one branch for breakfast and another for lunch. “Now no homeless person gets turned away,” he says. Social Bite also gives away any food it hasn’t sold that day when it closes at 3pm.

But the mission of Social Bite – whose food costs about the same as Pret a Manger and Eat – is to be much more than an upmarket soup kitchen. The first cafe opened in August 2012, the idea of Littlejohn and his then-girlfriend Alice Thomson. They were, Littlejohn says now, “clueless”: his experience amounted to studying economics at Edinburgh University and watching his father, Simon, who owns restaurants across Scotland. The inspiration for giving away their profits came from Muhammad Yunus, the Bangladeshi social entrepreneur who pioneered microlending.

It hadn’t been the plan to employ homeless people, but a Big Issue seller called Pete stationed himself outside the shop and, after a couple of weeks, he asked Littlejohn and Thomson for a job. Pete handed out leaflets for a couple of hours a day and then, when a position opened up, he became a pot washer. He also moved in with Littlejohn and Thomson to their one-bed flat while they tried to find him somewhere permanent. The experiment worked and Pete recommended his brother Joe. Littlejohn and Thomson set a goal that a quarter of Social Bite’s employees should come from homeless backgrounds.

Meeting this criteria as a small business has been a challenge; in fact, many days it’s a nightmare. No-shows are a recurring problem and new hires are prone to storming out. “It’s extremely chaotic to get them to fit into the employment environment where they have to turn up every day,” admits Littlejohn.

But for some the job has turned their lives around. One of these is 51-year-old Colin Childs, who was Social Bite’s third employee from a homeless background and now works filling focaccias in the central production kitchen. Childs had been a drug addict and had not had steady work for more than 20 years. “I’ve seen a lot of people come and go,” he says. “They can’t handle the work, they are used to dossing about the street or whatever. But Social Bite gives you the tools to change your life and it’s up to you if you want to take it. And I took it.”

For Littlejohn – Thomson remains on the board, but is no longer involved day to day – the secret is “endless chances, endless patience”. He shakes his head, “When I think of some of my staff and the challenges they’ve had to overcome to still be on their feet, you start looking at them with awe rather than, ‘For fuck’s sake, you’ve slept in again.’ You’re still standing – that’s amazing!”

When Littlejohn launched Social Bite, he had plans for 100, maybe even 500 cafes in the UK: “We thought, ‘Let’s take on Starbucks!’” He has since decided that five shops – two each in Edinburgh and Glasgow, one in Aberdeen – will better allow him to consolidate the work with his staff.

He has also launched a craft lager called Brewgooder, which donates all its profits to clean-water initiatives, and in September he, along with business partners, opened a more formal restaurant in Edinburgh named Home. This also employs people from the street and encourages donations from diners in the form of meal promises; every Monday afternoon, the doors are then opened to feed the homeless.

As for future marketing stunts, how do you top DiCaprio?

“There’s not many places left to go,” Littlejohn concedes.

Then he smiles, “Obama would be the obvious one. It sounds funny but it’s not beyond the realms of possibility.”