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What is perhaps most remarkable about the i3 is that it pulls off the amazing trick of looking like nothing else, but still looking like a BMW. At just under four metres in length, it’s barely any longer than a supermini like the Ford Fiesta or Volkswagen Polo, but with its two-tone paintwork, U-shaped running lights and exposed carbon fibre on the roof, it’s a very distinctive car indeed. The base version has big 19-inch alloy wheels, where the S versions swaps these for 20-inchers and comes with a few other subtle visual tweaks besides.

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Inside, too, the design is thoroughly original, despite containing several familiar BMW components. There’s a thoroughly unconventional mixture of shapes, materials, textures and finishes on show inside the cabin, but that gives the cabin a really appealing space-age feel, and the quality is properly top-notch. The upper dashboard is dominated by two colour screens – one directly behind the steering wheel, displaying information about the car (its speed, range and so on), while the other in the centre acts as the display for everything from the sat-nav, to the stereo and car settings. BMW hasn’t forgotten the basics, either: the driver has a good forward view out and plenty of adjustment in the driving position. However, the small rear window and massive rear-pillars mean reversing can be tricky, and the i3 feels bigger than it actually is when reversing into a tight spot, so parking sensors are an absolute must-have.

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The i3 is only a four-seater, but despite being a relatively short car, it has plenty of space inside, at least for those in the front. A cool design touch, the rearward opening back doors are nice in theory, but make getting in and out quite awkward, as you have to prise the front door ajar to get access to the cramped rear seats. Anyone sitting behind a tall driver will find the room in the back considerably less generous than in similarly priced rivals like the Audi A3 e-tron. With 260 litres (a little more than a Volkswagen Up), the boot capacity is reasonable for a car of this size, and the standard split-folding rear seats drop down to give a very decent, almost flat load area if you do need more space, but again, more conventional rivals are better at offering space for adults and bigger suitcases.

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A turning circle of less than 10 metres means the i3 is easy to manoeuvre through even the most congested city streets, but the question on many people’s lips will be whether the i3 drives like a ‘real’ BMW. The simple answer is that it does: with rear-wheel drive, a low centre of gravity and even weight distribution, it’s very well balanced. It will happily cruise at the legal limit on the motorway, too, and although you’re conscious of wind noise from around the door mirrors, that’s more because of the lack of engine noise than any fundamental lack of refinement. If there is a drawback, it’s the shortage of ride comfort, because the car feels rather jittery on bumpy surfaces, especially at low speed on the kind of city streets that most i3s will call home. The steering is also rather light and the weighting can be oddly inconsistent, which can take some getting used to. Still, it's fast and accurate enough to give the driver confidence when cornering,

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Like any electric car, the i3 is silent when you turn it on, but once you pull away, you’ll be shocked: the i3 is very quick and can beat most cars away from the lights. That can very useful (not to mention fun) around town, which is where most i3s will spend most of their time. Like any electric car, the i3 produces all of its torque immediately, which means it responds keenly and instantly when the driver hits the accelerator. What takes more getting used to is the strength of the regenerative braking, which slows the car as soon as you lift off the throttle. Mind you, it’s so strong that you can almost always drive through town without ever touching the brakes, which is actually more relaxing than it sounds. There are several driving modes to choose from, and if you pick the 'Eco Pro' or 'Eco Pro Plus' modes then your speed is automatically limited - to 70mph and 55mph, respectively - to help conserve the batteries. Of course, this is less of an issue if you pick the range-extender model – which has a petrol engine to generate electricity when the batteries are depleted - because you can simply fill it up with petrol and off you go again. However, the small two-cylinder motorbike engine is quite noisy when it does kick in.

There’s also an S model – available in both normal EV and range-extender formats – that ups the power of the i3’s electric motor from 170 horsepower to 183 horsepower. You can feel the boost in performance, making it feel like a very quick car, but it’s not like the regular i3 is some slouch.

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If you compare the i3 to other electric cars, such as the Renault Zoe and Nissan Leaf, it looks rather expensive. . Then again, many will argue that it’s also more desirable, and a lot of buyers will be more than prepared to pay the extra. What’s more, your investment will also be protected more effectively by stronger resale values. Go for the all-electric version, and you’ll get the same minuscule running costs and financial incentives that you do with all electric cars. And, if you need to go further than the car’s 125-mile range (which is pretty good by the standards of electric cars) can take you, you can pay a monthly fee to join BMW’s Access programme, giving you access to a range of other BMWs when your i3 isn’t suitable.

Then again, you could just buy the range-extender version, which will go a fair bit further, and which you can just fill up with petrol to keep you going. Yes, it costs thousands more to buy, but currently it’s a more realistic solution to electric motoring for more people. And, once you’ve bought the car, it’s still very cheap to run and comes with some of the same incentives. Unlike some electric cars, the battery is included in the price of the car, so you don’t have to pay extra to lease it. However, that does mean you’ll have to foot the bill when the time comes to replace the battery, if you keep the car that long.

No matter which version you choose, it’ll be cheaper to charge than to fuel a conventional car. It takes four hours to charge the car from flat to 80% using a home wallbox or ten hours from a regular socket.

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The i3 is too new for there to be much reliability data available, but in theory at least, it could be better than a conventionally engined car, as there are fewer components and moving parts. If you have concerns about the electric drivetrain, they may be partly allayed by the eight-year/100,000-mile battery warranty. However the range-extender is known to have had reliability issues with overheating, but only when driven on petrol power alone for an extended time - not what the i3 was originally intended for - so that's worth bearing in mind. BMW in general has a pretty poor record for reliability, coming flat last in the 2018 JD Power Vehicle Dependability Study.

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In theory, making the passenger compartment out of carbon fibre-reinforced plastic, which is exceptionally strong and keeps the occupants separate from the battery, should give the car excellent safety. That’s why it’s all the more disappointing that the i3 scored only four stars (out of five) in Euro NCAP tests. The testers said that, in the side pole impact, protection of the chest was weak; the front seats and head restraints provided marginal protection against whiplash; and, the front edge of the bonnet gave poor protection for pedestrians. It’s also a bit disappointing, especially on a car this expensive, that you don’t get automatic emergency braking as standard, when you do on many cars that are much cheaper. To get it, you have to specify the optional Driving Assistant Package, which also gives you a function that automatically maintains your speed and distance in city traffic.

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The biggest choice for buyers is whether to spend the extra on the range-extender version, as both it and the electric car come with the same high level of standard equipment. This includes alloy wheels, Bluetooth, a DAB radio, sat-nav, rear parking sensors and climate control. Beyond that, you can specify optional ‘worlds’ for the cabin, which give you different trim, upholstery and floor mats, and you can choose from various combinations of three packages – BMW Maintenance, BMW Access and ChargeNow (public charging) – which are available for an additional monthly fee. The Volkswagen Golf GTE and Audi A3 e-tron have similar kit levels, and cost around the same as the range-extender, though, and both are better all-rounders. The S version adds the power upgrade and visual tweaks we’ve already talked about, but nothing in the way of luxury kit.

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If an electric car will fit into your lifestyle, then the i3 is certainly worth a look. Its price is justified by the premium look and feel, and fun driving dynamics, and there's nothing else on the road that looks like it.