Lunchtime. A man sits, alone, on the long concrete bench that runs the length of The Skirt Of The Black Mouth and eats salad from a Tupperware box. It has been raining, but now the sun’s out; its light reflects off the man’s fork, casting pale shapes onto the burnt black wood behind him.

For most of the day, The Skirt of The Black Mouth is a place people walk past. At lunchtime, it’s a different matter. Over sixty five metres of concrete bench and a table made from scaffold planks and metal struts offer a place to sit, and the people come: a flock of birds that descends, rests, and then flits away again. They come with their brown paper bags, their cardboard containers, their Tupperware and plastic-wrap. They come on their own – read a book, scan their phone, listen to music as they eat. They come in pairs, sit angled towards each other and talk about work, about the weekend, about family. They come in groups – three, four, five, six – bags and food wrappings, crisp packets and drinks bottles multiplying around them, the sound of their conversations rising and falling over the noise of a lorry reversing; drilling from the building site; a bike creaking with each turn of the pedals.

She went out with a chef for a while. At the start, he tried to teach her to cook, but she never did things quite the way he would and they’d always end up fighting. Now she works two jobs – pulling pints in the pub at the end of her road; interning at a magazine. She hasn’t the money to buy lunch every day. She hasn’t the time to make it.

They sit under one umbrella, the rain tapping at the fabric, and eat the sandwiches he made that morning – ham and cheese on wholegrain bread. ‘It’s like camping in Wales,’ she says, scrunching the cling film into a pale, almost blue lump. He has never been camping in Wales. He kisses her and wishes he’d known her childhood self.

She sits on the concrete bench, her back angled to match the fold of the slatted wooden wall, and holds her phone in one hand to mark out her touch-screen space. She’s bought chicken salad – less calories than a wrap, a Panini, a baguette. The lettuce is crisp and cold, slick with balsamic dressing. He hasn’t texted her back. She spears a cherry tomato with her plastic fork and waits.

I ask people what’s the best meal they’ve ever eaten, and invariably we end up talking more about friendship and family than a particular recipe or ingredient. ‘It comes down to the gesture,’ David Matchett, development manager at Borough Market tells me – to someone cooking the same chocolate cake for your fiftieth birthday as they cooked for your tenth; it may not have been made with the world’s finest chocolate, but it transports you.

She left home thirty years ago. When she goes back, her mother calls wanting to know what she can prepare. She asks for soup. ‘Soup? I want to make a feast for you,’ her mother says. ‘Please, just one of your soups. Chicken broth. Vegetable. There is nothing like your soup.

He grew up with the smell of his gran’s baking. Soda bread on the griddle pan, the furrows of a plate’s edge across its top. The weight of potato farls. Flour on the tip of his nose. He grew up with bread. Broken. Blessed. Shared.

The Feasting Mouth, designed by artist collective Exyzt, consists of a table to gather around and an oven to bake in: simple ingredients designed to bring people together. Local community groups are invited to come and feast. They make pizzas or bread in a workshop run by baker and designer Alex Bettler. Alex uses the process of making, baking, sharing and eating food to enable conversations about identity, about city-living, about how and what and where and why we eat. Food puts people on the same level, he tells me; we sit around the table to eat and we are equals. For him, food – and in particular bread – is a tool to communicate, to make friends, to connect.

‘This is Barbados.’ He gestures to his pizza – the sea smeared with pesto, the coast-line marked in slices of red and orange pepper. ‘I grew up here.’ He points to an olive, then to a line of split yellow peas, ‘And here are the best beaches.’ She can picture him – a boy, the sun on his skin, the sea breeze ruffling his hair.

‘We’re campaigning against lunch at the computer.’ The man wears a pink tie with tiny flamingos dotted across it. The top button of his shirt is undone. ‘I cook for him sometimes.’ He points across the table to where his colleague eats from a plastic box of tuna pasta. ‘When I’ve time.’

A group of West Indian veterans make and share pizza with residents from the Blackfriars estate. They design their pizzas as new flags for London, share stories about the West Indies, about London, about the war, their families, their lives. The space is buzzing. The oven is hot. Passersby cluster on the pavement to watch. Public space becomes private dining room; a shared lunch turns into an unrehearsed performance.

Lunchtime at The Skirt Of The Black Mouth is a space and a time that holds the potential for connection and conversation, community and sharing. And at the same time, it suggests an individualised, private approach to lunch – singly wrapped sandwiches, a box of salad for one, sitting in a line on a concrete bench, using a phone, an iPod, a book, to shelter us from the world.