Most people who reach for the phone to call for an ambulance or a fire engine think they know how it's supposed to work. They'll dial 999, get connected to the appropriate service, give their address, then wait for the screaming sirens. Faced with a life-threatening crisis, your field of attention narrows drastically; if your husband's having a heart attack, or your child has stopped breathing, nothing matters besides executing the sequence of steps that you believe will bring aid. So it's common for emergency telephone operators to encounter bafflement, and even anger, when things don't unfold as expected. "Just send the ambulance!" people sometimes shout, as the call-taker works through a scripted list of questions designed to identify what's happened and what first aid advice should be given. "Just get off the phone and send the ambulance!"

In fact, if the system is working properly, the ambulance or fire engine could already be on its way: a dispatcher will have been listening in to the call, making rapid decisions about which teams of paramedics or firefighters to send to which emergency. The role of the call-taker, meanwhile, goes far beyond merely asking for the address. Between the two defining moments in a crisis - the moment when normality ends, and the moment when help arrives - lies a terrifying expanse of time, of minutes that seem like hours. As you wait for the sound of the sirens, the operator on the other end of the line may be all you've got.

The extraordinary 999 transcripts reproduced here, with the consent of those involved, don't have much in common with each other: the five-year-old boy reporting his mother's epileptic fit, the woman giving birth at home alone, and the man whose neighbour has sliced his own arm off seem to share only their sense of urgency and panic. But all the conversations demonstrate how much is demanded of the call-takers. At a distance, and without being able to see what's going on, they often must explain to untrained strangers how to carry out life-saving medical procedures. At the same time, and no less importantly, they're frequently the caller's only human connection during the long, edgy minutes before the emergency crew arrives. "The first-aid instructions are scripted, but the bit you can't do from a script is the bit that actually gets the caller to follow your instructions," says Mark Myers, a London ambulance service worker who writes a compulsively readable blog at Neenaw.co.uk. (Mark Myers is a pseudonym.) "We're trained with various techniques, but a lot of it's just intuition: what does this person need to hear? What's the thing that's going to get through to them?"

One thing that rarely seems to get through is the fact that help's already coming. "It's on the way," the operator repeats to Steve Francis, in Telscombe Cliffs, as he struggles to stanch the bleeding where John Stirling's arm has been severed by a chainsaw. "It's only round the corner ... it's just coming now." The news seems to cause astonishment. "Yes. It's literally round the corner ..."

Surprisingly, perhaps, call-takers are relatively junior in the hierarchy of the ambulance control room. (The dispatcher's job - which involves making snap decisions about how to spend NHS money - is more senior.) Charlotte Wright, one of the call-takers featured here, was only 19 last December when John Swift called to report that his wife Ruth, who has multiple sclerosis, was lifeless after choking on a sandwich. At the time, Wright had been working for the ambulance service in York for barely two months. "I think she's gone ... Be as quick as you can, because I think she's dead," Swift says in the recording of the call, his voice trembling. There was no time to wait for the paramedics. Wright talked him through the Heimlich manoeuvre over the phone, and Ruth survived.

There's no trace of panic in Wright's voice on the tape, and a year after the event, she recalls it matter-of-factly: talking to her, you're reminded that there are simply some people who are cut out for this kind of work, and some who aren't. "I suppose there was adrenaline rushing through me, because choking's quite a time-critical thing, so you have to act fast," she says. "But you don't panic. If we panic, we're absolutely no help to the caller. It's difficult to explain, but you do just keep yourself calm."

Throughout Wright's exchange with Swift - as in all the other calls here - there are ceaseless words of reassurance: "You're doing really well ..." "You're doing so well ..." "You want to be really, really proud of yourself ..." This is a central tenet of the call-takers' training: it keeps callers calm, and improves their ability to deliver first aid. ("It made all the difference to have someone encouraging me," John Swift told the York Press afterwards.) It's also a way of staying upbeat without succumbing to the natural urge to reassure callers that everything is going to be all right; after all, it might not be. "I do remember taking a call that was given to me as a panic attack, and the husband was saying, 'She's dying, she's dying, please hurry up!'" Mark Myers recalls. "And I said, 'Calm down, calm down, she's having a panic attack. She'll be OK ...' Well, she did die. It wasn't a panic attack. My words echoed in my head for some time after that."

The emotional impact of working the phones only usually makes itself felt in the gaps between calls, or at the end of the day. Counselling services are available, but usually it's just a matter of collecting one's thoughts: Danielle Holbrook remembers taking a few minutes to recover - to breathe - after the call she took from five-year-old Jakob Seviour as his mother lay unconscious in an epileptic seizure. For Theresa Ross, the Cardiff operator who helped Sarah Leismeier deliver her baby, the impact came when she heard its first cry. "I was just awash with relief," she recalls.

Of course, high drama is the exception. A regular shift might involve tens of routine calls, and several aggravating ones: a hoaxer, perhaps, and plenty of people tactfully described as "uneducated users of the service" - those who think a sore knee or a mild temperature is a worthy reason to request an ambulance. But exchanges such as the ones featured here - in which frightened people are successfully guided back from the brink of debilitating panic, so they can deliver themselves or their loved ones to safety - more than make up for all that. "I worked in customer services for 17 years before this," Theresa says. "It's hard to describe how satisfying this job can be sometimes."

• Read the transcripts and listen to recordings of the emergency calls here:

The birth

The epileptic fit

The fire

The cardiac arrest

The Heimlich manoeuvre

The amputation