You remember your first. Mine was in 1978 – a turquoise flash zipping low over a murky Oxfordshire river. A moment in the eyes, a lifetime in the memory.

I’ve seen plenty more kingfishers since then, but you never spurn an opportunity, and the Water of Leith – a tranquil haven minutes from Edinburgh’s centre – fits the bill. Just over 20 miles from source in the Pentlands to outflow into the Firth of Forth, it has earned its reputation as Edinburgh’s hidden jewel. You could spend a month here and never suspect its existence, yet for the initiated it offers respite from the relentlessness of fringe season.

The Water of Leith, flowing through Dean Village in Edinburgh. Photograph: K Neville/Getty Images

Upstream, there are otters tumbling in the stiller waters outside the Scottish National Gallery of Modern Art; downstream, a tern colony watching over Leith Docks. Here at Stockbridge, a heron stands patiently on the bank, straggle-bearded with a dagger bill. The city’s bustle is just up the hill, a thousand miles away.

Once part of Edinburgh’s industrial heartland, with more than 70 mills lining its banks, the river’s shallow waters now run clear, home to thriving fish and invertebrate populations – and that means birds.

A dipper sits on a midstream rock, brown plumage matching the peat-stained water, white chest catching the eye. Portly yet nimble, it hops down, plunges below the surface, and walks along the bed. Most songbirds don’t do this. But most songbirds don’t have solid bones, nasal flaps to stop water going up their nose, or a milky-white third eyelid – a “nictitating membrane” – to protect the eyes. A special bird, the dipper. This one rummages with nervous bobbing movements – then it’s off, like a dumpling late for a dentist’s appointment.

A heron at Water of Leith ‘with a dagger bill’. Photograph: Lev Parikian

And where there are dippers, grey wagtails often follow. Grey above and yellow below, their tails pump constantly as if plugged into the mains. Two of them cavort in the shade by the water’s edge – irrepressible, irresistible.

Up the rise towards Dean Village. All I need to complete the walk is oh look. A turquoise flash – a time-traveller from 1978 – zips low over the water. It lands, sits, still. But not for long. A darting foray and up it comes with a wriggling silver sliver. Sit, dive, fish – a stunning trifecta of kingfisheriness.