A day out in London sees Jason Goodwin having a run-in with a car wash, paying tribute to a 20th century genius and ending up a prisoner of modern technology.

I couldn’t help thinking, as I stared through the steel bars, that things had escalated very fast. One minute I was punching my credit card details into my mobile phone, the next, I’m a prisoner on a London street.

My friend Anna had suggested the underground car park. Garage spaces in Westminster go for the price of a country cottage, but Anna had a ruse. Deliver your car to the car-wash people in the morning, go back to collect it in the evening and you’ve had free parking for the price of the wash.

It might be called bucking the system, or gaming the car park, but, in my case, it failed because the nice men at the car wash were only too ready to do the car right then, giving me no chance to drop the keys and disappear up the fire escape. I drove away cursing and, in a side street, Googled car parking.

It meant downloading an app, but, for a mere £12.50, I bought a day’s parking close to New Scotland Yard. I received an email with the address and a photograph of nondescript grey-metal gates. On arrival, the email said, I should type in a location code fastened to the gates and they would open up to reveal my parking slot.

I pasted the address into my satnav, pausing en route to admire the back view of 55, Broadway, the HQ of London Transport and winner of the 1929 RIBA London Architectural Medal, which had been opened up by demolition. Its architect, Charles Holden, later built the Senate House in a similar stone and style and many suburban Tube stations.

St James's Park underground tube station and the art deco period building above, 55 Broadway, London’s first skyscraper

St James’s Park underground tube station and the art deco period building above, 55 Broadway, London’s first skyscraper

It was briefly the tallest building in London, with a frieze by such luminaries as Eric Gill, Samuel Rabinovitch and Henry Moore. Jacob Epstein’s sculptures Night and Day caused outrage when they were unveiled. Newspapers campaigned against them and one Underground director offered to have them removed at his own expense.

The hero of the hour was that great public servant Frank Pick, who ran London Transport in its heyday between the World Wars. Pick wasn’t only an administrator of genius – Pevsner called him Britain’s leading 20th-century patron of the Arts. He declined a peerage, but accepted a Soviet honour for helping them build the Moscow Metro and he gave the Underground its unique and familiar appearance.

He stuck up for Epstein and even offered to resign over the issue, which was finally resolved when the irascible sculptor agreed to hammer 1½in off the penis of the smaller figure in Day.

One of Jacob Epstein's sculptures at 55 Broadway London Underground Headquarters, London

One of Jacob Epstein’s sculptures at 55 Broadway London Underground Headquarters, London

The car park lay below a block of flats nearby. The gates were already open so I drove in. That was my big mistake. I got out of the car, just in time to see the gates close automatically behind me. In front of me was a set of steel shutters, which didn’t move.

The app, when I checked, had no idea that I’d arrived – it was still waiting for me to tap in the code from outside.

It was then that I discovered that I couldn’t read it from inside. I put my arm through the bars and tried to angle the phone to take a picture of it, but it was too low down. The gate was too high to climb. All of a sudden, the street seemed deserted.

Standing helplessly between two steel gates, I had a vision of our future, in which driverless cars that can’t distinguish between shadows and toddlers go rogue, their software in the grip of 14-year-old Moldovan hackers, while people like me gaze sightlessly from the kerb, parking apps our living tombs, frantically scrolling through FAQs that we haven’t asked and for which nobody has an answer anyway.

Where’s Frank Pick when you need him?