Our cities must have been dreadfully foul and smelly before the motor car. At the London Transport Museum they have a display of two horse-drawn vehicles. Pre-recorded voices make it sound like the model horses are chatting to each other, and there’s fake horse dung on the floor for extra giggles. Whole sub-industries flourished in clearing up the straw and excrement clogging up our 19th-century streets. It must have been particularly grim when it rained or snowed.

I thought about this exhibit while trying to cross the road the other day, waiting for a break in the relentless London traffic. I watched cars whizz by, spewing out fumes that we know are toxic, and burning fossil fuels that costs us millions to extract from the ground.

It struck me how awful and primitive that is going to look in a museum display in a hundred years’ time. People stuck in movable boxes polluting the air, taking up all the space in our cities. The display will calmly inform people that by the early 21st century, thanks to huge efforts expended on safety measures, only around four people every day died on the UK’s roads due to cars.

That is the way things are.

But technology is going to transform it over the next couple of decades, and we can see the endgame. We know we are going to get to a point where nearly every car is driverless, and uses some kind of rechargeable electric power rather than petrol engines.

There will be awkward decades where the modes of transport co-exist, as evidenced by the fact that one of Google’s self-driving cars just pranged a bus in the US. But what is the exception now will become the norm. The Manchester Guardian reported on the first fatal motor car accident in the UK back in August 1896. You wouldn’t dream of reporting on a non-fatal road collision now unless it featured a new technology like Google’s. Or a celebrity.

What interests me though is the way that the driverless revolution will transform our urban spaces, and the routes between them. Nearly everything about urban road design is currently done to minimise the risk of humans making bad decisions.

Take traffic lights. You’ll still need road-crossings for pedestrians and cyclists, but in a world where every vehicle is controlled by computers, algorithms should be able to feed vehicles through junctions faster. No more sitting at the lights waiting while literally nothing wants to cross your path. The need for traffic lights gradually fades away, in the same way that we no longer have inns where you can pick up fresh horses. Motorway junction design, roundabouts, urban parking spaces: all of these things could and will be profoundly changed.

And then there’s the way that we behave inside cars.

For the last century the interior design of the car has been entirely optimised around one person with feet on pedals and hands on a wheel, with their eyes to the road and their need to have all the controls within easy reach. But if you don’t need a human in charge, then the very layout of the seats in a car can be fundamentally reorganised.

A driverless vehicle might have people sitting facing each other, with a table in the middle. Or the front windscreen could show you all a movie while you are travelling. Or there might be self-driving cars configured as sleepers, so you can go to sleep in one city, and wake up in another, while remaining in an enclosed private space.

It is still a way off. Government consultation documents in the UK about “the pathway to driverless cars” indicate that for now vehicles will need “a test driver present” who “takes responsibility for the safe operation of the vehicle”.

But once society lets go of the fact that “driving” in itself is an activity that requires attention and time, people will pretty quickly cotton on to the fact that being in driverless cars is a way of increasing your leisure time. And, presumably, your working time. The business that buys a fleet of driverless cars knows that staff can be doing paperwork between meetings while they travel, for maximum efficiency.

We still tend to describe these new vehicles as “driverless cars”, defining them by what they don’t have, just as the “horseless carriage” seized control of our roads a century or more ago.

I read a brilliant piece the other day by Benedict Evans about the evolution of smartphones, and it had this phrase in it which has stuck in my mind: “People in the ‘middle ages’ didn’t know they were living in the ‘middle ages’.”

As I stood by that roadside the other day, watching all these inefficiently routed cars containing people that had to be fully attentive on controlling them, and knowing that they were poisoning me as I stood, I thought of that phrase again. Truly we can look to the future of the car right now, and know that we are currently in the middle ages of mechanised personal transport.