With its 252bhp 2.0-litre turbocharged engine, the four-wheel-drive supermini can complete the 0-62mph dash in 5.7 seconds.
To make this possible, Audi has taken the rear axle and engine from its hot TTS coupe and squeezed it into the A1.
In normal driving most of the power goes to the front wheels, but the system can divert up to 100% of drive to the rears if required.
Just 333 examples of the A1 Quattro will be made, with only 19 cars heading to the UK all of which will be left-hand drive.
Whats it like to drive? Despite its less-than-remarkable 0-62mph time of 5.7 seconds, the A1 Quattro feels rapid in real-world driving. Part of this is thanks to the added drama of the fantastic, growling soundtrack played out by the engine and exhaust system.
With most of the power heading to the front wheels, the A1 has an initial tendency to understeer when thrown at a corner. However, as the drive is shifted to the rear wheels, the car is more than willing to hang out its back end when provoked. The steering is responsive in such situations, but is short of total precision.
Despite all of the work that has been done to the suspension, the ride is not too firm easily soaking up the few bumps we found.
Whats it like inside? There is no such thing as an options list for the A1 Quattro, so each car is identical and fully loaded with everything imaginable.
This includes bespoke 18-inch alloys, Glacier White metallic paint, sports seats complete with Quattro badging and red stitching, large twin exhausts, a prominent rear spoiler and red painted wings in the headlights.
Other touches that mark the Quattro apart from the standard car include a red-faced speedometer.
It also comes with air-conditioning, light- and rain sensors, DAB digital radio, sat-nav with Google maps, and a Bose stereo with 14 speakers.
The new rear axle system cuts into the boot space which has shrunk from 270 litres to 210 as a result but the cabin is unaltered, so there's just as much room in the rear as in the standard car.
Should I buy one? If you could, then we'd absolutely recommend you buy one. However, the A1s 41,020 pricetag is a hefty hit given this is still an Audi supermini. Running costs possibly won't be of much interest to buyers of such cars, but it averages 33.2mpg and emits 199g/km of CO2.
However, if the costs don't put you off, what might is that Audi already has deposits for all UK-bound cars. So, it's a case of waiting to see if any owners want to part with theirs in years to come.
What Car? says