The river has a gift for us today. It has fallen back so deeply, the low tide so low, that the whole shoreline is laid bare, calling to us.

I don’t know why we decided to come this way this afternoon, our daily walk breaking free of its usual tight turns of the park. Her hand in mine, we’ve drifted down the middle of the empty roads, hopped on and off pavements, dodged joggers, to end up here, our invisible bubble of space popping against the river’s edge.

We’re where Black Lion Lane runs right out into the Thames. No wall, just a gap, an alley of thin air. Across it, a set of steps, a few up, then down, right into the river. Usually the brown water is three steps from the top; the river swirls wide and fast and greedy here, curving up to Hammersmith bridge. But today, it is sunk to a ribbon. The steps lead all the way down. At the bottom, brick squares make a pathway to the shingle.

She tugs my hand. ‘C’mon, Mum!’

The steps are slick with grey mud trodden up by others. ‘Stick to the side, look,’ I tell her. We strike out onto the brick patches, wobbling across the sludge. The river-smell is thick here, all salt and mud and dirty knickers. When we’re onto dry pebbles, the wind catches us. The clouds are whipped huge overhead, the sunlight feels astringent. After the past few weeks, the space hits us like a hey presto, like a huge glass cloche, lifting off.

The shingle is deep, gives underfoot. We crunch over treasures. Clam shells, river glass, really good skimming stones. Someone has heaped bricks in formations on the river bed. There are mounds of metal things, rusted together. A cairn of beer bottle shards. My girl wonders if everything is either Roman or Victorian. She points to the opposite bank. Made small by the distance, there’s a man waving a metal detector along the water’s edge.

‘It’s called mudlarking,’ I say. ‘You can get a special license to do it.’

‘Is this Victorian?’ she asks.

It’s a small chunk of pottery, a piece of plate, broken off from the edge. Blue and whitish, pattern made vague by the water.

‘No,’ I say, smiling. ‘It’s a bit like one my Nanna used to have.’

Not exactly heirloom stuff. Nanna would have bought it in the late forties, after the move to Kent. After the bomb had smashed whatever crockery she’d had in Upton Avenue. Everything made rubble, the house fallen around her, her father under it. She’d left East Ham with my small uncle in tow, not looking back. Her London was exactly diametric to ours. You’d see it if you pressed the map in half. Great grandmother and great granddaughter: two girls, two lives, opposite sides of the city, a century apart. On the same overlapping spot. A vivid fleck of blood, transferred across generations.

I take pictures on my phone, as we turn and face the wind, walking up towards Hammersmith. Lately I’ve become obsessed with photographing the sky. As if reminding myself there’s an up; somewhere limitless. A way out.

She’s raced on ahead, my daughter, the plate-bit in her pocket. While I’ve not been looking, she’s undone her hair, and her ringlets lash in the wind. Her legs have grown stalky over the tops of her wellies. I take a photo of her, kicking along the very edge of the water, dancing where it ripples. When you realize your baby is a mermaid-hair gangle-shanks, I think, ridiculously, in Instagram captionese.

In this cloistered spring, this time trapped apart, at the river’s lowest ebb, everything looms oddly, the perspective all out. The bridge ahead looks tiny. The people on the Thames path are toy soldiers on a battlement. And my little girl is suddenly writ large. Herself, only – more so.

She’s always surprising, always unexpected, this gift of mine. Now she’s off, running full pelt, the distance all hers. I follow behind, feet careful on the shifting pebbles, watching her surge headlong into the day.