Take a look at Ferrari's new exhibition

You might not be able to picture the Ferrari J50. It was unveiled late last year, a very pretty rebody of the 488 Spider. Only ten were made, all for Japan (that's the J part of the name). What chance of seeing one in London then? Every chance actually, as the full-size styling model is part of a Ferrari exhibition at the Design Museum, opening today.

The show is called Ferrari Under the Skin, and it's been mounted, with factory support, to tie in with 70th anniversary since Enzo started making cars under his own name. The total value of cars here is £140 million.

The show is an eclectic but very helpful canter through the history: the man, his engineers and drivers, the road and race cars and how they were made. It's not comprehensive – how could it be? – but it's nicely balanced across the ages. It manages to feel like an exploration and critique, not merely hagiography.

You start with a look at Enzo, through walls of fabulous original photos – many I'd not seen before – and artefacts such as factory plans and even his actual driving licence.

Another segment shows how the cars have come together. There are blueprints and styling drawings of all ages of course. But more space is given to the actual stuff they once used to get the bodies right: wooden bucks, full-size wire-frame models, dismounted aluminium shells, and latterly, wind-tunnel models. And then that lovely J50, one side of it naked clay, the other side pained to look tantalisingly drivable.

If your fetish is for mechanical entrails – mine is – then you can enjoy a good selection of castings, engines (in whole or lovingly dismantled to an array of components) and gearboxes and chassis.

And you can get within touching distance – but please don't touch – of cars you've seen pictured a thousand times. Among them are the ex-Schumacher F2000, Nick Mason's F40 registered F40 NPG, Giovanni Agnelli's silver Testarossa Spider, the ex-Peter Collins 250 Cabriolet, the green David Piper 250 GTO, and the Stirling Moss 250 SWB in that beautiful Rob Walker scheme of dark blue with white nose band.

At the entrance is a perfect recreation of the first open V12 Ferrari, the 125S. At the exit, the latest, a white LaFerrari Aperta that belongs to Gordon Ramsay. You can get closer than you ever would in the fetid crush of a motor show. Guess that's the advantage of this being art not commerce.

The exhibition runs to 15 April 2018, and it's £18, with good discounts for concessions and families.