"In the wild," Maxwell says, "a horse's predators are cats and dogs. Dogs can't grab a horse around the neck like a cat can, but what they'll do is to try to bite it near where its stomach meets its back legs. If they can make a small incision in the flesh there and open the stomach wall, the intestines will begin to fall out and the pack will simply follow the horse until it falls over. In the starting stalls, the running rail which the jockeys put their feet on touches horses in that area, and some of them just can't tolerate it, their instincts tell them to get the hell out."
When it's put that way, you wonder that any of them go in at all, and still more at how Maxwell ever manages to persuade the difficult ones otherwise. He is the consultant to whom Henry Cecil, Michael Stoute, John Gosden, David Loder and several other leading trainers turn when one of their valuable young charges turns out to be a problem child. The average horse weighs in at half a ton, and Richard Maxwell tips the scales at 160lb, but when he tells them to stay put, they do.
Or rather, they do eventually. Maxwell has sometimes been portrayed as a semi-mystical figure, a sweet-talking cross between Dr Doolittle and the Marlboro man, whose every word is heard and understood by his equine patients. The reality is rather different. Maxwell's techniques rely on repetition, habituation, and long, patient hours of one-to-one work.
Maxwell is a disciple of Monty Roberts, the American expert on equine behaviour who designed the thick rug, worn over the horse's sensitive area, which allows a handler to gradually introduce them to the stalls. His theories on "communicating" with horses - in essence trying to understand how and why they react to certain situations and keeping this in mind when attempting to change their behaviour - first came to Maxwell's attention during his time as an officer in the Household Cavalry.
"I had to ride horses which had been broken using the Monty Roberts method," he says. "The previous year, when they hadn't, I was getting thrown off and hurt, but with Monty's method we did 35 horses and I didn't get thrown once. There were all types of horses, but they all behaved in exactly the same way, and it was a revelation to me, it was like being born again. I feel so much more at ease now with what I'm doing."
After leaving the Army, Maxwell went to California to learn Roberts's techniques from the man himself, returning to Newmarket 18 months ago to set up as, in effect, an equine psychotherapist. The Roberts approach to breaking horses still attracts Luddite suspicion among many at Headquarters, but Maxwell's work with starting-stall phobias has had such consistent success - 11 out of the 12 horses he has worked with at Warren Place, for example, have gone on to win - that few now doubt its worth. Vettori, this year's French 2,000 Guineas winner, and the Group-class performers, La Confederation and Stelvio, have been among those to benefit.
But it can be dangerous work too. As we talk, Maxwell is working at Henry Cecil's stable with a two-year-old filly whose aversion to the stalls is such that she is at present unraceable. Now, after four hours' work in recent days, he has persuaded her, with the help of the comforting rug, to walk into a wooden stall. He asks her to stand there, moving a step or two back and then forward to become accustomed to the touch of the running rail.
All the time, her body language is loud and fluent. "As she goes backwards, her eyes open and her blinking slows right down because she's worried something might be going to get her. When she snorts, it's just anger. And when she starts licking and biting, she's trying to be submissive. If she's eating, or pretending to eat, she's not worried about her immediate safety, but at the moment she's finding it very difficult."
Just how difficult is about to become clear. A sudden noise startles her and she is off away, dragging Maxwell behind her as he clings grimly to her halter. She rears, bucks and kicks, but he refuses to let go. After a frantic 15 seconds, she relents, and Maxwell leads her back to the entrance to the stall. The process begins again.
"It's been a real learning process for me too," he says, "stood here when one of them runs at you. I've been knocked to the floor a few times. But you have to try and keep yourself controlled. Sometimes I've been stood at the end of this rope and felt the horse's heart beating through it, they're that terrified. If my heart's racing, she'll feel it and her own will go up too."
Forty-five minutes later, the filly will stand in the wooden stall for two minutes or more, and her drooping head shows that she is slowly becoming accustomed to the process. Yet still, there is a long way to go - an hour each day for perhaps four weeks - before she will be able to face a full set of metal stalls amid the noise and stress of the racecourse.
It would try the patience of many, but Maxwell is undaunted. "The tougher they are, the more involved you get," he said. "Stelvio, who won the Queen's Vase, that boy put me through murder. One time something triggered him and it was like being tied to Mike Tyson in a broom cupboard, he battered the hell out of me.
"But when I saw him gallop past the post at Ascot . . ."