Immortality could be sneaking up faster than we can believe. Barely a month goes by without some new advance in organ replacement, and a recent operation to replace a boy's windpipe with one generated from his own stem cells was called "embarrassingly simple" by the specialist in charge. Further breakthroughs could be made by the Sens Foundation, led by the radical immortalist Aubrey De Grey, with a brutally simple plan to give humans an unbeatable protection against cancer. This involves limiting human cells' ability to divide at cancerous levels, with regular top-ups from externally grown cells replacing worn-out tissue.

If these technologies can hold to their promise, biological immortality, perhaps the most cherished goal of the transhumanists, may be with us in a few decades. A loose grouping of scientists, philosophers and sympathisers, with organisations such as the Oxford Future of Humanity Institute and Humanity+, transhumanists urge human progress through radical technological enhancement. With regards to immortality, I'm certainly a sympathiser: if a dictator was murdering tens of millions of people right across the world, we'd gladly do anything to overthrow him. And yet ageing, as eloquently put by the transhumanist philosopher Nick Bostrom, is a tyrant that kills us by the cartload – and what do we do to stop it? And yet most people remain unconvinced by the possibilities laid out by transhumanism, saying that even if it's possible, it's unethical.

Certainly, an immortal future would not be a perfect utopia. Deadly accidents would still happen. Society would still be riddled with flaws, foibles, sorrows and absurdities. We would have to deal with those, as we always have done. At an individual level, people worry about their health, avoid the red meat counter, and spend a fortune on supplements while grinding themselves to a pulp in the gym. All these tiny tweaks add but a few years to your life and come at a cost of time, money or sensation.

Leftwingers decry, with some justification, trickle-down economics as crumbs from the rich man's table. Yet what is reaching for the olive oil, or heading down to the gym, other than trickle-down life expectancy? A year here, a year there. Crumbs from the table of the gods. It is possible that the relative equality of death appeals, but the differences in life expectancy are not great compared with the enormous differences in personal wealth. Giving that up for agelessness, which could open vast gulfs between the billionaire and the builder, would be to some opponents a step too far. Francis Fukuyama has criticised transhumanism for just this reason, arguing that it could lead to a truly monstrous class system. Yet virtually every modern society makes great efforts to provide healthcare to everyone, regardless of income. Why would immortality be different? It's the ultimate in healthcare, after all.

Another barrier to a more widespread acceptance of transhumanism is population control. Even if we can secure an equitable provision of immortality, be it drugs, tissue replacement or something else, critics would contend that population numbers would explode and that we'll soon be living in a crowded, polluted dystopia. And yet the longest-lived societies have the fewest children. Why would this trend not continue as an industrial society becomes an immortal society? If you could expect to live for thousands of years, how many centuries could you wait before having children? After all, it is perfectly possible that we could end up in a crowded hell-hole even without immortality.

Imagine, years and decades from now, you are wretchedly ill with the diseases of old age. The only cure is to reverse the ageing process. And don't imagine this as an abstract philosophy problem. This is you. Would you say no? Would you turn down the chance to live again?

• This article was commissioned after readers suggested it in a recent You tell us thread. The author posts below the line under the username Anax