"Chatfield would normally lead the run and he would take us around London. We would arrive back after what Chaty felt was an appropriate time. There was always a rule - don't be last. You don't want to be last out to practice. Don't be last on the bus. Don't be last."
Essentially, the New Zealand squad ran themselves. Indeed, when Bob Vance, the manager, was taken ill early in the tour and returned home, his duties were shared out between the players; Bruce Edgar, the opening batsman, doubled as the team's treasurer.
After the first Test in 1986, a hard-fought draw, Mike Gatting famously said that facing New Zealand was "like the World XI at one end, and Ilford second XI at the other", such was the gulf between Richard Hadlee and the rest of the attack.
"It was a little demeaning," Coney recalls. "It was a motif throughout that tour."
The players even got T-shirts with "Ilford seconds" emblazoned on, which they trained in.
New Zealand's 1-0 series victory was underpinned by the squad's resourcefulness.
The side batted deep and cussedly: seven players scored half-centuries, including Coney; three of those - John Wright, Martin Crowe and, from No 8, John Bracewell - hit hundreds.
Yet the win also bore the undeniable imprint of individual greatness. In the eight-wicket win in the middle Test, at his home ground Trent Bridge, Hadlee took 10 for 140 in the match and scored 68.
The victory in England was merely one of New Zealand's signature achievements during a magnificent decade. In 1985-86, New Zealand beat Australia in Test series at home and away. At the Gabba, New Zealand bowled Australia out for 179, and then declared on 553 for seven.
"The team were dotted like bait around the boundary at the Gabba. Every player, except the bowler and the keeper. We'd broken them. It was a real moment because New Zealand had been such a poor cousin."
In 1980, New Zealand defeated West Indies, the last series that West Indies lost for 15 years. The first two Tests were played in the windswept South Island: "The heaters were mysteriously lost," Coney laughs.
New Zealand's victory was a fraught one-wicket win in the opening Test in Dunedin, sealed through "the two worst leg byes you've ever seen in the world" when their No 10 and No 11 - Gary Troup, a sports distributor, and Stephen Boock, a supermarket manager - were batting together.
Before New Zealand toured the Caribbean in 1985, Coney knew that the phalanx of West Indies pace bowlers would leave him no time to play booming drives. "I'm going to need strong forearms - not big flowing shots, just punchy shots. So, how do I strengthen my forearms?"
Coney's answer was unorthodox. He got an empty four-litre paint tin, and added lead head nails to make it heavier. Then, he attached the paint tin to a broom. While watching TV, Coney lifted the paint tin towards him and then back down again - like a bucket - for an hour at a time.
"You develop the muscles between your elbows and your wrist," he explains.
"You make the best of what you have around you - and some of those solutions might seem a bit odd."
The ploy worked: in the four Tests, Coney averaged 48.2. Such self-reliance was New Zealand's hallmark. "We were still edging out of being a cottage industry."
New Zealand Cricket's secretary kept boxes - containing everything from minutes from board meetings to the team's caps, socks and cricket balls - in his garage.
"There's a hardness about the amateur or semi-pro. An amateur doesn't wait for someone to tell him something. What he does is he thinks ahead, he thinks 'jeez, I've been there before, I know what this requires. I am going to be an outfielder, therefore, and be useful to my team'."
Before the tour of Australia in 1985, Edgar put lead inside cricket balls to make them heavier, training to throw the ball on the longer Australian outfields; during the Test series, Edgar ran a batsman out with a throw from the deep.
"We were practically-based - and we had to be.
"Playing for money, what are you talking about? We played for the love of what we were doing."
Yet, while Coney managed to navigate his parallel careers well enough to average 37.6 in his 52 Tests, he would have liked to have been able to devote himself completely to cricket.
"Would I have liked to have been a pro? Yeah, of course. I would have liked to have some of the information."
Coney credits Wright, Crowe and Hadlee, the three pros on the 1986 tour, with teaching the squad aspects of the mental side of the game.
For all his brilliance, captaining Hadlee was not always easy. Before New Zealand's last Test against West Indies in 1987, Hadlee used a newspaper column to have a "wee crack" at his team-mates' professionalism.
"It was ghosted, of course, but the team felt he'd overstepped; not by saying it as much as by not saying it face to face. We had all agreed to keep things like that inside the dressing room. I had to have a word. But in the next Test, he took six for 50 to help draw the series. He was a great bowler."
It ensured New Zealand were undefeated in all Test series at home throughout the 1980s.
Asked how his New Zealand vintage would have fared against the team who won last year's inaugural World Test Championship final, Coney chuckles.
"Our side, with Bracewell as a spinner, with Hadlee and batsmen who watched the line so closely, like Edgar and Wright and Crowe - I'd give us a chance."
The Sunday Telegraph