When a food festival runs out of food, is it a sign of success or failure? Actually, I'm being a bit disingenuous. It was only in the very last hour that some of the chefs taking part in last weekend's Let's Eat Glasgow, the UK's first 'socially inclusive' pop-up restaurant and producers' market, had to take some dishes off their menus.

In the producers' market (so-called to differentiate it from a farmers' market) fishmonger Andrew Vallance sold out of fresh West Coast langoustines and scallops within hours, and Peelham Farm's charcuterie – chorizo and red wine salami – came close. People were queueing to sign up for Locavore's veg box delivery scheme and Urban Roots' meal bags were finished by the end of the day.

And that, surely, is a good thing.

At certain moments, though, it was hairy. Such was the inaugural festival's unimagined popularity that just two hours in on the first day – a Saturday of blazing sunshine – alarm was already mounting that the restaurant food was about to run out.

Chefs could be heard screaming into their mobile phones to their suppliers. Please can we have more ox cheeks? Can you bring me more langoustines and scallops? Others were dashing back to their restaurants for more food. At one point customers were being asked to be patient while more food was prepped. At around 1pm on the Sunday the queue of people trying to get in backed up into the street.

But what an astonishing, wonderful problem to have.

Logistics were always going to be a challenge for Real Food Real Folk, the not-for-profit co-operative of independent chef-proprietors behind Let's Eat Glasgow. After all, they'd never done this before. They were working off-site and running their own restaurants in town at the same time.

Each of the seven restaurants devised three plates at £5 each. They'd planned for 6000 dishes between them, but in the end they served 10,000 plates to 7000 visitors.

The blips didn't last long. They were dealt with swiftly and professionally, and taken in good spirit. It seemed to me, on my three visits over the two days, that a sense of surprise and awe overtook everyone. This was really happening. Glasgow, once known as the sick man of Europe, had pulled off one of the coolest, funkiest, inclusive food festivals.

Let's Eat Glasgow marked a UK first: admission was free, and all profits (still being calculated as we went to press) are to go towards helping the city's less privileged. One thousand meal vouchers were donated to food-related social enterprises in the city's more deprived areas such as Govan, Milton, Ruchill, Clydebank and Shettleston, and at least 500 of these vouchers were redeemed. The producers and chefs tell me they encountered lots of new faces, asking interesting questions. One said that 95% of the customers he had over the weekend had never been to a farmers' market.

This indicates that Let's Eat Glasgow achieved extraordinary success in its aim of reaching a new demographic from outwith the middle-class foodie-forward West End, and for this it should be applauded.

The original idea was to hold it in the old Cattle Market in Dennistoun in the city's east end, but a suitable agreement could not be reached. Perhaps Glasgow City Council might support this idea next time around; suspending existing catering contracts for council-owned property would also help widen the choice. The privately-owned SWG3, on the other hand, offered a warm welcome.

The twin aim of the festival was to showcase the great food that is being both produced and cooked in Glasgow. Real Food Real Folk was formed out of frustration that Glasgow doesn't properly market itself, and is not marketed, as the foodie destination it has become.

Food was cooked to order on site. Crab Shakk's spicy 'Singapore (North Uist) style' pincer end crabclaw meat and sticky riceball had run out by the time I was in the queue. Cail Bruich's Loch Duart hot smoked salmon with avocado smear and tiny pickled cucumber balls was divine (I'd wanted to try the hay-smoked ox cheek with celeriac but didn't get the chance).

I loved Ubiquitous Chip's roast Renfrewshire wood pigeon with an Argyll forest barley risotto (the Lochlibo shrubbery that accompanied a monkfish and scallop carpaccio and the pickled Ayrshire chioggia beets and Lochlibo baby cucumbers on a platter of West Coast meats were from the restaurant's allotment).

Friends reported that The Gannet's cold-smoked scallop was also excellent. Ox and Finch's roast pork belly with shredded thai salad, peanuts and prik nahm pla; and a home-smoked mackerel served wafer-thin pickled fennel and radish were sublime. Mother India's Bhel puri with coconut salmon was good; Guy's trio of mini Scottish (as opposed to Scotch) pies were dinky little packages of softest beef steak, haggis with clapshot and smoked haddock with cheddar.

Some restaurants were offering complimentary shots of 18-year-old single malt along with their dishes. Although this did add to the atmosphere of joyful conviviality, I'm not entirely sure it was necessary. Do Glaswegians really need such sweeteners to encourage them to eat well?

There was some jokey speculation that some people even used their meal vouchers for this purpose alone; a great example of Glasgow's sense of humour.

Long may it flourish.