Jemima Lewis: I've seen the future in my grandmother's plight

It's a terrifying prospect: a million centenarians by 2074, with half of them suffering from dementia

It used to be a source of great pride to me that my grandmother was not like other old folk. Long after my friends' grandparents had succumbed to dementia, disability or death – or simply slid into beige-clad invisibility – the Lewis family matriarch remained, in body and spirit, uncannily young.

A farmer's daughter with a duchess's sense of social superiority, she had no sympathy for her fellow pensioners, whom she regarded as incorrigibly drab. She shuddered at the Crimplene ghosts who crept along the promenade of her seaside town, hunched over their tartan wheelie trolleys. And I, gazing in awe at this least grandmotherly of grannies – with her strong, tanned limbs, her stylish bleu de travail tops, scarlet lipstick and favourite earrings made from two tiny flies trapped behind glass – couldn't help but share some of her contempt for those people weak and unimaginative enough to grow old.

Now that decrepitude has finally caught up with her, I suspect (no, hope) that I feel the humiliation more deeply than she does. At 94, after a series of strokes and a spell in hospital with a broken hip, Granny is now unmistakably geriatric. Everything about her, from her hair to her voice, is thin and wasted. Her teeth have rotted away to a few blackened stumps. Once a brilliant cook, she subsists off pulpy ready-meals blasted in the microwave, which she sucks down with apparent satisfaction. She cannot bathe, dress, or put herself to bed without help – this Amazon who once chased away a grizzly bear while camping in the Canadian forest, and who taught a tribe of Native Americans the useless English art of riding side-saddle.

Cruellest of all is the way that deafness and creeping dementia have cut her adrift from social intercourse. Her essential personality – mischievous, unsentimental, witheringly frank – emerges here and there, like the sun peering out from behind the clouds. "You are much less distinguished-looking than your sister," she told me last week, and it was like being enfolded back into the arms of a long-lost loved one. But most conversations with her are either maddeningly circular or fall abruptly into silence, as if she were too exhausted to keep trying to make sense of the misheard, half-remembered world around her.

So far, Granny has been able to stay in her own cottage thanks to my aunt Julia, who commutes from London to spend half the week with her, and a tiny savings account – the result of a lifetime of making do and mending – which is being plundered to pay for part-time home help. But we all know that it cannot be long before a nursing home, and the accompanying financial crisis, beckons.

The Government announced this week that it is to review the way care for the elderly is funded. Means-testing, introduced by John Major in 1993, has always hit people like my grandmother hardest: those who, while not at all rich, have managed to scrape together enough for a little house and an even littler nest egg, both of which must then be sacrificed to pay for the care-home bills. Relatives like my aunt, who may have given up work to look after their parents at home for as long as possible, lose even the compensation of a modest inheritance. Labour's suggestions for remedying this situation are so far exceedingly vague – a consultation document here, a hint of extra public funding there – and no wonder. Britain's greying population is already putting a serious strain on the public purse, and the situation is only going to get worse.

Dr Guy Brown, a Cambridge neuroscientist, warned this week that "the future is not just old, it's extremely old". Thanks to better nutrition, healthy living and medical advances, babies born in Britain today can expect to live to 100. The total number of British centenarians is set to rise from 10,000 to one million by 2074 – with at least half of those pensioners suffering from dementia. As Dr Brown points out, massive funds will be needed to pay for new drugs and "round-the-clock care for decades on end for millions of demented or disabled people".

It's a terrifying prospect, and one we have entirely brought upon ourselves: first, with our addiction to privacy and space, which means that we are no longer willing to live with and look after extended family (especially of the incontinent or interfering kind); and second, with our determination not to die.

The narcissistic modern cult of healthy living starts to seem quite insane once you have witnessed senectitude at close quarters. After her hip operation, Granny was temporarily dispatched to a nursing home to recover. It was as cosy, clean and friendly an institution as one could hope for, but it was still a vision of quiet misery. The fluorescent lighting and chipped magnolia paint; the inevitable fug of cabbage and urine, exacerbated by stifling central heating; the cadaverous inmates sleeping with their mouths agape in front of the communal telly. "Nobody talks," confided Granny in a rare moment of lucidity, "and they peck at their food like little birds."

This is the future we are buying for ourselves, with our low-fat, non-smoking, antioxidant life choices; our gym memberships and germ-busting kitchen sprays. In hoping to live for ever, we are fashioning ourselves a living death.