This government-backed lottery has enjoyed a renaissance in recent years. Today, more than 23 million people hold bonds worth a staggering £27.1bn in total.
In the 12 months to April this year, some £5.7bn of them were snapped up by investors hoping that Lady Luck would bestow a tax-free £1m jackpot. Yet that figure is actually a big fall on the £7.5bn invested the year before.
Hence a decision by National Savings & Investments (NS&I), the body that runs the lottery-cum-savings vehicle, to up the ante with its recent marketing campaigns and new incentives for investors.
From this month, each draw will have two £1m prize jackpots.
On top of that, Sir Alan Sugar, the tycoon who made millions from Amstrad computers and went on to present the hit television series The Apprentice, has been hired to promote the bonds in a TV and newspaper campaign.
"They're tax free, no risk. You can always get your money back," he purrs on screen.
Technically, he's correct. If you gave NS&I a stash of £1 coins to invest on your behalf, but won nothing, you would get the same number of coins back if you later cashed in your stake. But the advert makes no mention of premium bonds' major drawback as a financial product: your money is not protected against inflation.
Any rise in the cost of living can make significant inroads into your investment. Say you buy £10,000 worth of premium bonds today, when inflation is running at 2.3 per cent (its highest since 1997; see page 23). Leave them there for 10 years and win nothing, and your money will be worth just £7,920 in real terms, assuming inflation stays at this rate (a calculation based on figures from independent financial adviser Bestinvest).
Cross your fingers for another decade and, with the same rate of inflation and lack of good fortune on your part, your £10,000 would be worth £6,280.
Premium bonds pay no interest at all - so your only return will be from prizes if you're lucky enough to win. For these reasons - inflation, no interest, a need for good fortune - concern is growing that the advertisements for premium bonds don't fairly reflect the risk attached to them.
"There should be some sort of warning to investors to suggest that their capital could be eroded in real terms after the effect of inflation," says Paul Ilott of Bates Investment, an independent financial adviser (IFA).
Patrick Connolly of IFA John Scott & Partners agrees: "Mention of inflation should be there in the adverts ... and bigger than the small print."
Their comments reflect rules drawn up by the City regulator, the Financial Services Authority (FSA). These dictate that, if a financial product is particularly affected by a single factor, then any adverts for it should reflect this.
"If inflation was a major issue for a product, we would assume that it would be made clear," confirms an FSA spokesman.
The threat is acknowledged by NS&I. "There is the possibility that inflation can have a greater impact [on your investment] if you don't win anything," a spokeswoman concedes.
However, NS&I denies that its adverts' declaration of "no risk", and failure to highlight the menace of inflation, run contrary to this rule.
"The issue of inflation was assessed and not referred to in the advertisement as the term 'no risk' is based on [there being] zero risk to the [customer's] nominal investment," says the NS&I spokeswoman. "We don't feel [inflation] needs to be made clear in the advert; it's as clear as possible."
Premium bonds also have a handy get-out clause for not sticking to the regulator's guideline rules: they don't have to. Because they are backed by the government, they fall outside the FSA's remit.
The only form of regulatory test that the TV ads featuring Sir Alan had to pass before going public was to be approved by the Broadcast Advertising Clearance Centre. They were given the green light.
In fact, the rules that premium bond adverts follow most closely come under the Code of Conduct for the Advertising of Interest-Bearing Accounts (CCAIBA), published by the British Bankers' Association. This makes clear that inflation does not have to be mentioned as part of an advertisement for such a financial product.
But premium bonds are not interest-bearing products: they reward consumers with tax-free prizes instead.
NS&I says it complies voluntarily with the CCAIBA: "With premium bonds, you're gambling on your return - the average punter accepts that."
Rather than paying interest, premium bonds have a "prize rate" - linked to the Bank of England base rate - that determines the return on your investment if you enjoy "average luck". But this simply reflects the size of the bonanza available each month and is meaningless for those who don't win anything.
Last week, the premium-bond prize rate dropped from 3.25 to 3 per cent.