One by one, the legendary figures of a golden era – Stirling Moss, John Surtees, Tony Brooks, Jackie Stewart – rose from their chairs to pay tribute to one of their great contemporaries. Above them as they stood at the microphone was a giant black and white photograph of the late Jack Brabham, captured in a moment of glory as he celebrated one of his 14 grands prix victories. Addressing a large audience gathered at Silverstone for a memorial to the three-times world champion, who died earlier this year, his old rivals recounted the still-compelling tales of their battles on the track.

But it was later in the afternoon that the best story of the day was told by a man in his late 60s, whose name would be known to few outside the inner circles of motor racing. This was a story that, in the end, said a lot about how Formula One has changed in the past half-century.

Nick Goozée was a 13-year-old south London schoolboy when his father took him to watch a race meeting at the old Crystal Palace circuit. His attention was drawn to the spectacular driving of a man who had arrived from Australia a few years earlier, had found a job as a mechanic and had climbed the ladder that would lead to the world title. That day, the boy became Brabham’s No1 fan.

A few years later he discovered Brabham had set up his own racing team in a garage not far from his home. At the start of a school holiday he hung around the building until he was invited to come in and help with sweeping the floor and making the tea. It became a regular feature of his life and when he left school in 1963 his father went to Brabham to ask if there might be a permanent job for the boy. Yes, he was told, and if the boy did well with the basic tasks, after five years he might become a mechanic.

By the end of the decade Goozée had become one of two young men responsible for building the triple champion’s cars and maintaining them at races around the world. In those days, a couple of mechanics was all it took. Goozée remained devoted to Brabham – a famously taciturn figure who, he recalled, seldom said much beyond “G’day” and, after trying out some modification or other: “She’ll be all right.”

Brabham hung up his helmet at the end of the 1970 season and returned to Australia. A couple of years later the operation was sold to Bernie Ecclestone and soon Goozée was accepting an offer to join the team of the ambitious American businessman Roger Penske, a former driver. From a base in Poole, Goozée would supervise the building of cars that carried the Penske name to serial victories at Indianapolis and many other US tracks.

The other young mechanic who had worked alongside Goozée on Brabham’s car, a fastidious young chap called Ron Dennis, also did well for himself. Dennis now runs the McLaren empire – including its Formula One team – from a spectacular £200m headquarters designed by Norman Foster. Dennis’s career, like that of his former colleague, shows where a proper apprenticeship would once get you, if you were made of the right stuff.

Their equivalents in today’s F1 are the people with doctorates in aerodynamics who will be sitting at computer screens in the McLaren technology centre during this weekend’s US Grand Prix, crunching data and transmitting the results across 5,000 miles to the engineers on the pit wall, who can then instruct the driver on precisely how to modulate his engine’s fuel consumption and when to come in for a change of tyres.

They are also the dozens who turned up for work at the Caterham team’s Oxfordshire factory the other day to find the gates locked by the administrator. Caterham’s two cars will not be on the grid at the track in Austin, Texas this weekend. Neither will those of Marussia, their equally hard-up Oxfordshire neighbours, also put into administration this week and facing possible closure.

There is, of course, no natural law saying a Formula One grid has to consist of 11 teams and 22 cars: just Ecclestone’s law. The historian Doug Nye reminded me this week there were only 13 starters in the Spanish GP of 1968. Graham Hill won that race – and, as Doug said, nobody asked for their money back.

Many teams have vanished during the 65 seasons since the start of the world championship, from big names such as Maserati, BRM, Alfa Romeo and Porsche to smaller ones such as Connaught, Scarab, De Tomaso and AGS. All were mourned but others arrived to fill the gaps. The fear now is that, through a combination of wanton profit-taking and neglectful governance, the men who run the sport have made it virtually impossible for new entrants to come in and thrive unless they are either major manufacturers, like Mercedes-Benz, or super-rich businessmen with a product to advertise, like Red Bull’s Dietrich Mateschitz.

As that well-known socialist Max Mosley said this week, Formula One is simply too expensive and the financial rewards are tilted too heavily in favour of the leading teams – a process that may have begun when Ecclestone, Mosley’s old accomplice, started paying Ferrari a bonus in order to ensure the presence of the sport’s most charismatic team, with their unmatched box-office appeal.

The nature of Formula One means the odds have always favoured competitors who can afford the high cost of cutting-edge technology, whether in the 1950s or the 21st century. But by inviting the designers to frame the technical regulations, Ecclestone and the governing body have allowed the sport to run out of control. No technical director of a well-funded leading team would voluntarily make a serious effort to level the playing field, or propose a truly radical move such as removing the immoderate influence of aerodynamics on the design of the cars.

Instead they come up with gimmicks and half-baked regulations such as the one that limits the number of engines each driver can use in a season, which will lead to Sebastian Vettel, the world champion, starting Sunday’s race from the pit lane, since he has already used up his permitted allocation. Like so much about modern Formula One, it defies rational explanation and the sort of common sense that once made it a sport in which someone such as Nick Goozée could start at the very bottom, sweeping the floor, and make his way to the very top.