The very important man on the other end of the phone broke off abruptly from our conversation.

“There’s one straight over my head at the moment!” he shouted with barely controlled glee. “It’s scared of landing on the building. It’s a young one, it’s swooping around, just beautiful.”

I did not want to bring Lyndon Parker, Senior Events Officer of the Royal Society for the Protection of Birds (RSPB), out of his reverie and back to mundane matters. He was caught up in the exhilaration of watching the fastest creature on the planet hunting for its prey.

At speeds of up to 200 miles an hour, this small apprentice was manoeuvring deftly, teasing the air currents, flying low in a pigeon populated paradise.

But he was not in some remote Somerset field, or a Scottish mountain region; my contact was standing next to the Millennium Bridge, in the heart of London.

A stone’s throw from the Square Mile live four inner city peregrine falcons, accomplished urbanite raptors which have found a handy podium from which to hunt the river: on the towering chimneys of the Tate Modern.

They dine daily on alfresco suppers of plump London pigeon; and they’re giving the aerial display of a lifetime above the Thames, to anyone who has an hour or two and a little patience.

The RSPB has its tabs on the brood, and has a mobile centre and a bank of telescopes with which to entice passers by.

Peregrine falcons are cliff dwellers. Where there’s no cliff, the sheer face and scale of a cathedral will do.

But this family has chosen the chimney of the Tate Modern as a perch: because it resembles another geological formation.

Lyndon said: “From their point of view, the Tate Chimney is a geological formation called a ‘stack’- something that used to be an arch like Durdle Door in Dorset, and the middle has collapsed.

“We saw some stunning hunting from one of the youngest birds over the Millennium bridge. The river is used by lots of birds as a highway to navigate by, moving up and down stream. Up on their perch the peregrines can see whats out there – and swoop.”

Lyndon is a regular down there, chatting with members of the public who stop and stand and stare, even in this busiest of cities.

He tells me with wry amusement that so many of the passers by ask, with genuine puzzlement, how on earth they keep the falcons up there on the chimney for the entertainment of the tourists.

For many of us, that’s how we see them: the rescue bird who has been trained to work with man.

Falconers may have been at their occupation one way or another for some four thousand years. They tend to be endlessly patient bird-whisperers who respect the nature of their hawks.

And they need to: because a hawk does not bond with a human like a dog or a cat. Affection is not part of the bargain. Trust is, though: experience tells the hawk that its trainer will provide a tasty lure and protection for hunting services rendered. And the falconer trusts the hawk that it will return.

The trappings of the trained peregrine falcon are necessary, but blunt: a hood to keep the falcon calm, strips of leather- called jesses -and bells on the legs, an identity band and sometimes a transmitter.

Writer TH White, who rewrote the Arthurian legends with such potency, became captivated by the art of falconry and trained a goshawk. Afterwards, he wrote about it with an authority born of experience. His reasons for wanting to undertake such a venture are quoted in the foreword of the resulting work, ‘The Goshawk.’

He says: “I had two books on the training of the falconidae in one of which was a sentence which struck fire from my mind. The sentence was: ‘She suddenly reverted to a feral state.’

“A longing came to my mind that I should be able to do this myself” he adds. “The word ‘feral’ has a kind of magic potency which allied itself to two other words: ‘ferocious’ and ‘free’ .”

Ferocious and free: and yet still tethered. And yet those urban falcons on the banks of the Thames are utterly wild. And that, says Lyndon, is their charm.

“When the peregrines are there, and we can show people through the telecope – I know when people have seen it through one of our telescopes – you can tell by their faces. People are just amazed that they’re in central London.

“A lot of people think they’ve been introduced by us: but they’ve come of their own accord. They are the fastest animal on the planet so they have that lovely wildness. They are phenomenally good fliers: a falcon’s element is the air and there’s a wildness to it.”

Should you find yourself on the banks of the Thames one Summer afternoon, it is entirely possible you might see something quite unique: the aerobatic focus of a creature which is quite the fastest, wildest urban city dweller London has ever known.