I’m yet to see a zombie movie that portrays the most likely way that a post-apocalyptic world will play out: hungry pensioners roaming around; not yet dead, but no pension to keep them fed, looking for an arm to gnaw on. If you think I’m being disrespectful to elderly people, I’m not: that’s my future I’m talking about. Wednesday’s Royal London report, suggesting millennials need to save £260,000 for a pension, is exactly the sort of thing that could lead to me one day eating the arms of my offspring. People who don’t expect to own a home will need to pay in £445,000 to live on a basic income – up from £150,000 in 2002-03.

But Steve Webb, Royal London’s policy director, assured me on the phone that it’s not all gloom and doom. In fact the solution is so not-gloomy there’s an acronym for it, because nothing bad ever gets afforded an acronym, except the way to deal with a stroke. The acronym is Sum: “Start as quickly as you can; up your contributions when you get a pay-rise; max out on what your employer will give you by putting more in,” says Webb.

This gives me little comfort as I contemplate the average £10.5k a year I’m supposed to be forking out for the next 42 years but don’t have. Neither, I imagine, does it help the many young people who won’t own a home in their adult lives. “I have to be constantly conscious about money. If I buy a coffee, or don’t make my own lunch one day, or have something other than Super Noodles for dinner, I can’t afford a drink at the weekend,” says Eloise Fry, a student in London. Saving is the last thing on her mind – Fry scrimps on luxuries, such as washing her clothes (“I have to pay £3 for it, it just feels painful”) after moving to the capital to do a master’s in journalism and taking out a £10,000 loan.

The bulk – £9,600 – of Fry’s loan pays for a tiny room in London (of 104 “journalism jobs” listed in her home town, not one was based at a paper; a London search returned coveted positions at the Guardian and Vogue). She sleeps pushed up against a pod with a toilet in it that she can smell from her bed. A sofa in the kitchen is her living-room; her heating is sporadic and her water frequently runs cold. But it’s not how much she spends that prevents her from paying into a pension – it’s debt.

Q&A What is a millennial? Show Although precise definitions differ, broadly speaking millennials are those people born between the early 1980s and the late 1990s. They are so called because they turned 18 in or after 2000. They are also collectively known as Generation Y

Left reeling from a student loan that didn’t cover her costs, she is now thousands of pounds into her overdraft. Just paying back the interest and the career loan will cost her around £400 every month. She isn’t making a dent in what she owes, let alone contributing to a pension. “How can I think about saving when I don’t have the money to pay what I already owe,” she asks.

Individuals didn’t always shoulder the responsibility of their own pensions – as Webb says, employers used to provide them as a given: “In the 90s, the stock markets were soaring and it was easy for businesses because if they put a pound in for you, it shot up the next day.” Today, with young people able to make the decision themselves, some millennials lucky enough to have started paying into their pensions are taking the money back out. Another millennial I spoke to landed a £19,000 job after two degrees and a master’s, but paying her pension had left her with £600 a month after rent.

She doesn’t regret opting out: “I have noticed a significant difference. Even if I have a pay rise I won’t restart, because I still can’t afford quite basic stuff like work trousers or a haircut.” But she didn’t realise she’d be offered her contributions back – a princely sum of £1,500. She struggles over whether she should withdraw that, too, to deal with her debts. “What I earn doesn’t pay off my overdraft,” she says. “I’m in minus money pretty much from the day I get paid. That scares me more than having an extra £1,500 when I retire.”

So basically, millennials such as me should be bloody depressed. Today was my rent day, and despite owing only £400 in rent, I was £330 short. The other £70 came from selling an old phone for a quarter of what I bought it for; and the rest came in the form of a loan from my 22-year-old sister, who has an overdraft and is on her way to racking up £50,000 of student debt.

Actually this emboldens me a little. What is anyone going to do if we keep just ignoring this looming crisis? In the future, won’t we be old enough to pass our burdens on to the next generation, just like the previous generation did to us? Or will there be an epidemic of zombie pensioners, and if so, will I get a film credit for the first movie about it?

“No, no, you’ll just have to miss out on what average people do – no foreign holidays; no fixing your car if it breaks down,” says Webb. Oh, right, that’s it? “Mate,” says Fry, at her liveliest since the beginning of our conversation, “I’d trade foreign holidays for clean clothes any day.”

• Poppy Noor is a Guardian columnist and commissioning editor