It was to be the face-off the world has been waiting for; the duel between the two greatest road cars, the like of which will almost certainly never be seen again in an oil-hungry, emissions-regulated, eco-friendly world.

Not since Ben Johnson took on Carl Lewis in the 1987 Rome world championships, or Muhammad Ali rumbled George Foreman in the sweltering heat of the Zairean jungle in 1974, would two such evenly matched heavyweights contest the right to be the greatest. And where better for the Bugatti Veyron to meet the McLaren F1 than the Nürburgring in Germany, scene of some of the most awe-inspiring races in history.

That, at least, was the plan. Things started well: Bugatti would make the Veyron available. But the F1 proved more difficult. McLaren at first said it would be delighted to help. Then it had second thoughts and a PR lady called Ellen wanted to know what the F1 was going to be tested against. When she heard it was a Veyron an iron curtain suddenly descended.

“I have checked with our customer care department and I’m afraid that we are unable to help on this occasion,” said a final frosty e-mail. This is the effect the Veyron has on people. It is feared like a mythical creature.

The contest would have to take place in absentia. We would test the Veyron near the Bugatti factory in Molsheim, France, then fly back to Britain and drive a privately owned F1 on an airfield in Wiltshire.

McLaren’s concern was understandable (though it would have been braver to accept the challenge). The statistics for the Veyron are fearsome. Its 1001bhp engine delivers 922 lb ft of torque — three times as much as a Land Rover Discovery and yet it weighs a third less. At top speed it covers the length of a football field every second; truly it is a monster.

It has been claimed that the Veyron, named after a 1930s racing driver, is so quick that it could allow the F1 to start first and reach 120mph and would still reach 200mph first. In fact this claim is unfair to the McLaren — but not by much. You can let the McLaren reach 65mph and the Veyron will still beat it to 190mph before leaving it for dust.

That is not the only advantage the Veyron has in a straight fight with the McLaren. In every way — performance, build quality, ingenuity of design — it is the better car. It will fool you with just how well behaved it is, cruising quietly on B roads or nosing through the traffic. But it is cuddly in the same way as a polar bear. Put your foot down and it sprouts teeth and claws. It’s like being in a Ferrari F430 going through an Incredible Hulk metamorphosis. Being pushed back in your seat on the way to 60mph is one thing, but experiencing the same acceleration passing 160mph is a new sensation. The landscape becomes speed-blurred like a cartoon. Other cars appear to be going backwards. You expect to look in your mirror and see you’ve blown their doors off and sucked out their radiator grilles.

Flipping between gears with the steering wheel paddles takes just 0.015sec. The power delivery is seamless, the engine note rising from a deep burble like a powerboat tethered to a jetty to a howl like a Formula One car.

It’s hardly surprising the Veyron is the stuff of myth. Europe’s richest car company poured tens of millions of pounds into developing it in a fit of extravagance. Exactly how much, Volkswagen won’t say, but it was a lot more than poor old Gordon Murray had to spend when he was knocking up a prototype F1 back in 1992.

In 1998, the year that McLaren stopped production of the F1, VW bought the Bugatti marque. Quietly, it started going around Europe like Yul Brynner in The Magnificent Seven, recruiting the best component suppliers. What it was asking for was as far-fetched as using only seven men to defend a Mexican town from a small army: a transmission that didn’t disintegrate; tyres that didn’t explode; brakes that didn’t melt. Furthermore, every part of the Veyron had to be tested to engineering tolerances closer to those applied by Nasa than in car manufacture. Not too ambitious, then.

Remarkably, Bugatti got almost all it wanted. The seven-speed double-clutch gearbox is produced by Ricardo in Leamington Spa. The carbon-fibre monocoque chassis is from ATR, which also makes the chassis for the Porsche Carrera GT and the Ferrari Enzo. The body shell is spray-painted by Weiss, which has the contract for Maybach. The leather interior is stitched by Boxman, supplier to Bentley; the seats are by Sparco, which also supplies Ferrari and the World Rally Championship, and the brakes are made by AP Racing of Coventry, one of the most renowned suppliers of racing brakes.