And now Jean-Christophe Bolle-Reddat, creator of the Peugeot 20Cup (for that is its name), not only plans to take his toy out on the road sometime, as he did with his V12-engined 907 concept, but even likes the idea of a 20Cup race series along the lines of the races for the little mid-engined RC coupes. They, too, started out as a pair of concept cars.

There's no longer a pair of 20Cups, though. The white one got crunched at the Mortefontaine test track near Paris, and may not drive again. The black one is alive and well, however. And we've driven it.

On one level, the 20Cup is a bit of fun, a half-car with a hint of motorbike and a spectacle of total surrealism as it heads towards you and begins to turn. Where is the rest of it? I'm reminded of A View to a Kill, the Bond film featuring half a Renault 11.

On the next level, it reveals to the public the face, albeit hand-formed in carbonfibre, of the upcoming Peugeot 207 supermini, complete with smiling grille and slanty headlights. And on the third level, this proper, working concept car is powered by the hottest version of the 207's eventual engine range, a joint venture with BMW, also destined for the next-generation Mini.

It's a 1.6-litre, 168bhp, direct-injection petrol unit with a twin-scroll turbo (less lag thanks to no exhaust-pulse interference between cylinders), a self-regulating oil pump and a clutch-controlled water pump. With all that power, plus 177lb ft of torque from 1400 to 4000rpm, the sub-500kg 20Cup should be quite rapid.

It's raining here at Mortefontaine, so the racing tyres are wet-weather ones. The rear wheel is vast - it came from a Le Mans racer - and it sits between a pair of motorbike-like swinging arms, damped by a single Öhlins coilover. At the front is a fabricated double-wishbone arrangement, mounted on the engine cradle which in turn bolts to the carbonfibre monocoque whose scooped-out sides duct air away from the downforce-creating carapace of bonnet, front wings and cockpit surround.

There are, you'll notice, no doors. No windscreen, either, beyond a tiny transparent deflector. On with the helmet, then, and down into the deep cocoon of the cabin with its shoulder-level central rib. I'll come to curse this rib.

I'm strapped to the polystyrene seat with its gaffa-tape upholstery, the semi-rectangular steering wheel is refitted to the column, and a display magically appears in the wheel's centre. It currently shows lateral and longitudinal acceleration, selected gear and road speed, and it's supposed to stay level when the wheel is turned, but is a tad askew.

Start the engine and there's a healthy blat of not-very-silenced exhaust, although all the calibrations are said to be production-spec. Clutch down, press a button on the right of the steering wheel's boss to select first gear. There's the mechanical clunk of a race-type sequential transmission with dog-clutch engagement. Revs, clutch, off we go, with the juddering hysteresis typical of a race car's driveline.

Second, third and let's try full throttle. Where's the wheelspin? The torque-steer? Remember the high torque, the fly weight... but the 20Cup launches itself with a happy, if tuneless, bellow and now we're moving very quickly.

Shift down, turn at the end-of-straight loop and - ouch! - my right hand is jammed between the wheel and that rib. I really think the 20Cup could do with more hand space and a quicker rack.

Hand retrieved, I return via a slalom and discover that a single rear wheel is not conducive to entertaining throttle-steer. It all happens up front and oversteer is right off the agenda. I knew there had to be a reason for four wheels. We look forward to trying the rest of the 207 in March.