Maternal nocturnal worry number 57a: how are our offspring going to get their toes on any rung of the property ladder if they want to carry on living in London? I’m sure thousands of us mothers of young adults lie awake at 2.30 a.m. contemplating the fact that a one-bedroom flat in Leytonstone now costs £375,000. We curse ourselves for not having bought the whole house next door to us in 1989 when it was for sale for a third of that amount.

Last week I set out to find the cheapest flat for sale in Greater London. By ‘for sale’ I mean fully for sale, not a ‘shared ownership’ situation in which the buyer acquires 25 per cent of the property and the housing association owns 75 per cent, and the buyer pays a varying ratio of mortgage and rent, gradually ‘staircasing’ upwards towards full ownership. This sounds seductively affordable, but it can turn into an extortionate nightmare, because if any repairs are needed, the part-owner has to pay the full cost. It’s a brutally one-sided deal, to be steered clear of.

And by ‘flat’, I mean a flat available to anyone, not a ‘retirement’ flat for over-55s only, which tend to be the cheapest. Scroll down the Rightmove and Zoopla offerings in remote parts of outer London, stipulating ‘min beds: studio’ and ‘max beds: 1’ and you go down from the £300,000s, through the twos, to the one-hundred-thousands. This was what I was after: the flats (all of them leasehold) going for £160,000, and very occasionally £150,000.

I viewed properties at these lowest prices at all four compass points of Greater London, travelling by public transport and folding bike. What makes these properties cheap is not only that they’re tiny, but also that they’re hard to get to. I marvelled at the ruralness of the wooded cuttings on suburban railway lines, the charm of the babbling tributaries of the Thames near its outer ring roads, the sweetness of the occasional thatched cottage or 16th-century pub holding its own among the Carpetright outlets.

The village of Cowley, to the far west of the city, has not quite caught up with the fact that it’s now actually quite reachable from central London, thanks to the Elizabeth Line stopping at West Drayton. I cycled the 1.4 miles from that station, past the parade of shops, to the modern cul de sac of Waterside, where a friendly estate agent, Thea, met me. Enchantingly, although the Waterside flat I viewed was as minute as any flat could be, consisting of just one very small room plus tiny bathroom and kitchen lobby, it looked right down over the Grand Union Canal and its muddy towpath. It also came with its own parking space.

Thea drove me two miles to the picturesque village of Longford to view another studio flat in a block, this time beside a bus stop called Heathrow Close: an apposite name, because it’s a 15-minute walk to the arrivals hall of Terminal 5. So, in public-transport terms, easily accessible from Lisbon – but to reach it from central London you would need to take a bus from Hounslow West. ‘Stop the third runway’ signs were everywhere, and there was a roar every two minutes as planes took off.

I noticed that none of the residents in the flats Thea showed me seemed pleased to see me, or desirous to sell. This was because they were tenants who’d been given eviction notices by their landlords, who are all selling because interest rates have gone up so much and the regulations around rentals are getting tighter.

To reach New Addington to glimpse the £160,000 flat available in the far south, you need to take either two trams from Wimbledon, or one train and one tram from East Croydon. I chose the latter, relishing travelling on rails down the middle of roads, which feels like being in the outskirts of Vienna or Prague. Stopping at nine increasingly rural tram stations, we swooped through fields to the terminus, New Addington, where, in steady drizzle, I cycled the final 0.7 of a mile to a dreary block of flats plastered in squares of white cladding. I worried that this would be a very long commute for a young adult who had perhaps met up with a friend for a drink at London Bridge after work. After drying off in the Costa Coffee on the parade, I travelled back to East Croydon and Clapham Junction.

In the far east, I found a strange and almost lovable spick-and-span flat 11 minutes’ walk from Barnehurst station, between Erith and Bexleyheath – so really east-south-east. Again, this cost £160,000. Its upside was that its bedroom was separate from its living room. Though both were tiny, this felt like a big advantage after the one-room studios. The downside was that it was a funny little single-storey cuboid carbuncle glued on to the back of another house. Its lease was 89 years, so in 15 years’ time any young adult who bought it would need to start applying for a lease extension, which would cost a minimum of £10,000.

In the far north, I found the cheapest flat of all: £150,000, with parking, in Enfield Island Village, 12 minutes’ walk from Enfield Lock station, three stops north of Tottenham Hale, easily reachable from central London as long as the Victoria Line is working. Between two branches of the River Lea, Enfield Island Village has its own Tesco Express, as well as a row of covetable Victorian riverside cottages. Again, the flat was caravan-sized; the sleeping area, only just large enough for a bed, curtained off from the living space, and no room for a table anywhere, just a television and sofa. The service charge would amount to £2,000 a year on top of the mortgage.

Perhaps Generation Rent will decide, on balance, to carry on renting rather than buying a student-room-sized leasehold dwelling in the outer suburbs. Even the £150,000 ‘bargain’ does seem an awful lot to fork out for such tiny square-footage. Back to sleep we mothers go, no closer to solving the problem.