Simon Carr: As I plant, dig and hammer in my allotment, I can feel the roots of a different world

The sense that we are not merely modern constructs is enhanced by pulling a potato out of the ground

It's irrevocably middle aged, I assumed, to apply for an allotment. You can't pretend to be young any more among your potato rows, in your patched tweed coat and sleeveless sweater, digging slowly in the early evening. It's not what young people do. You can't dance with potatoes or smoke them. Leeks have very few hallucinogenic properties. Allotment sex doesn't exist. I hope it doesn't exist.

As it happens there are a few younger elements in my neighbouring plots. Maybe allotments are about to be discovered; maybe they're about to be fashionable. Like canals were, and ballroom dancing. Google tells me there was a National Allotment Week in the summer. There'll be TV shows and competitions soon. Maybe there are already.

If so, the Trap Grounds will be among the front-runners. It's one of the most engaging pieces of England I've ever seen. Hidden behind a screen of trees that border Port Meadow, it's what all allotments should be.

It must be about 10 acres. There are trees, which mean you can't see from one end to the other. That's the trouble with many city allotments: you can see from one end to the other. That's why I never liked them when I was young. They had an industrial feel to them, as though they were intensively used. Like a market garden. The allotment holders were actually hungry in those days, of course, and that led to contraventions of the amateur spirit. There's no lack of the amateur spirit round the Trap Grounds.

We have trees, and blackberry hedges and stands of Jerusalem artichokes 10ft tall. The complex reveals itself bit by bit as you wander round. If plots are planned, the plan is rarely apparent. The pathways interconnect and take you on a story, full of incidents and accidents. You can see great ambitions fallen into decay. You see love in action as plots are tilled, weed-free, with high beds bordered by attractive waste wood. It all combines in a collectively ramshackle individuality.

The sheds lean this way and that. There are scarecrows. We all leave our tools about. There is wildlife. The neighbourhood loiterer gets too drunk and shouts at people. A fat rabbit flops into a bush. Some plots are fully netted against birds; others have wire up from the ground to keep the badgers out. There's skylife too. That Speaking Clock bird that goes, "Pip! ... Pip! ... Pip!" You can tell the robin because he sits on a spade and cocks his head at you like in the picture books. Flights of ducks come in and out of the seasonal landing grounds in Port Meadow. And that VC10 flying in and out of Brize Norton always makes me stop and lean against something, looking up. And of course, the sun.

All allotments have a peculiarly British quality, but this is magical. The sun shines across a profusion of greens, browns, black tarpaulins and rotting carpet. You feel part of a different world. Not just the Great War food production scheme, or Dig for Victory. Something more ancestral. Victims of the Enclosures were given allotments to compensate them. And monks used to have their own little gardens like this. And villeins owned strips which kept things very cosy between the villagers.

It still exists, this mix of the public and private. You have property rights in your plot. It belongs to you. For the annual rent under a tenner, and as long as you keep the thing tidy, you can be there for 50 years (as some have been). And yet your efforts, your work, your plan, your vision are laid out for all to see. Passers-by, neighbours. It has a sense of privacy because it's yours to do with as you wish, and yet it's entirely public, and you are probably far more influenced by the prevailing culture than you think. (I, for instance, painted my shed Allotment Green rather than Scandinavian Beach House Blue.)

But every plot is different, as different as people were in the 18th century, before we got standardised. At one end, there are plots with waist-high weeds and a small circle of leeks in the middle. At the other, a professional commune has entirely enclosed its three or four plots with netting in the most ingenious structural combination of one-inch battens. Brunel couldn't have done better.

Compare and contrast this with the shed I built myself (sic). This cabin is made of nails, windows bought from eBay and 800 cans of No More Big Gaps. Other more attractive structures are even less ambitious, made with whatever came to hand. The English genius for comfortable gardening is all around. Nature has been directed with a gentle hand; no violence has been done to the landscape with straight lines or right angles. It's a world that George Orwell would recognise with pleasure, the world we thought had disappeared with the maiden aunts riding into the mist.

For a start, allotment measurements are supposed to be in the old measurements. We learned these at primary school, most resentfully. A plot is frequently measured in rods (or poles, or perches – they're all the same, as you know, if you're over 50). A rod is five and a half yards, of course. These aren't imperial measurements; they're as old as the people who've always lived here. It sounds Anglo-Saxon to me.

And then you get into the land by crossing train tracks north of the station. You open a gate and wheel your barrow across three or four sets of tracks. That's amazing in this day and age. Trains pass along at enormous speed, blaring their horns if they see you. How health and safety continue to allow this a miracle. And yet, if they tried to stop us from crossing there, I bet it would go to the House of Lords.

What else? The vegetables that come out of the ground may also be ancestral. Enthusiasts and eccentrics keep varieties alive that might otherwise have disappeared. And the cultivation can dip us into a culture that is hundreds of years old, thousands of years old. Things grow in very much the same way as they've always done. Why that is so refreshing is a mystery. But the sense that we are not merely modern, technology-dependent, gadget-wielding constructs is always enhanced by pulling a rare potato out of the ground.

So the therapeutic power of allotments must save the NHS billions. Digging, hammering, building and planting is a wonderful antidote to the mental illness we culture workers all suffer from (the severe deprivation of digging, hammering and planting).

Howard Jacobson is away