This isn't actually an M car, but don't let that bother you. You can feel the magic.
In the engine, for a start. It's not the twin-turbo 3.0 of the old 1-series M coupe, but the new-generation single turbo. But it's very nearly as powerful, at 320bhp. And with some M modifications to improve response and sound, it's all rather scintillating.
There's masses of pick-up right through the mid-revs, and it chases towards the 7000rpm red-line with a vim and a voice that hark back to why we loved the BMW straight-six in the first place.
Even when you don't change gear much, this is a really fast car. But believe me you will keep changing, because you'll want the sound of it.
The M folks also burrowed deep into the steering and suspension, changing the rack and the geometry at the front, and stiffening all the springs and dampers. Plus there are special brakes, and unique tyres, differently sized front to rear. No messing.
So you catapult down the road grinning like a loon. And then, wey-hey, a corner explodes towards you. The M135i has absolutely got the smarts to cope. The steering is super-direct but so well weighted and progressive that it's never twitchy. Grip is nearly unshakeable, and equally tight at both ends of the car. You won't break the back tyres' traction by accident, but if you want to do it deliberately, 320bhp will be there to help.
It might not be as hard-edged a car as the 1-series M Coupe, but it's close. And give it a break - the old car was £40,000, and this one is £30k. A real bargain. Especially as it's got a more modern, roomy and amenable interior.
This is the first of the new three-door 1-series, but soon you'll be able to get the three-door with all the engines. The M Sport body pack worn by the M135i will be an option on several of the smaller engines too, but you can tell the full M135i by its twin tailpipes and unique wheels.
So if it's not an M car, what is it? An M Performance Automobile. A mouthful, and even BMW M executives can't be bothered with it - they say MPA. An MPA is a car that sits between regular BMW cars and full-on M cars. The people at M aren't solely responsible, but they have an input.
And their input is, obviously, good.
In fact the M135i is better than I'd expected because the last M car I drove was the new M6, and that didn't have the simplicity and connection that I want from an M car. This not-M car does.
The other thing about an MPA is that it can use layouts that M cars are denied. For instance, MPA can be diesel, or they can be 4WD. So the first MPA car was the M550d xDrive, which is both diesel and 4WD. [OK pedants, the X6M and X5M are ‘proper' M cars in that they're made by M, and yes they're 4WD, but the base vehicles were 4WD too so they were never going to be RWD. And I don't think they actually fall within the spirit of what an M car is. C'mon, do you?]
So because the M135i is an MPA and not an M, it will also be available with xDrive by the end of the year. And as a five-door. Cars to give the next-generation Audi S3 some real hurry-up, we'd guess.