The second-smallest Premium Bonds holding ever to win the top £1m prize was £400, with savers with this amount winning the jackpot on two occasions, one in October 2008 and the other in January 2015.

Just 12 people holding £1,000 or less in Premium Bonds have scooped the £1m prize. Separately, the same number of people won the £1m jackpot in the very first prize draw in which their bonds were eligible, making them some of the luckiest players ever. Jackpot winners are visited by an NS&I official, known as “Agent Million”, who delivers the news in person.

No one with just one £1 bond has ever won the £1m jackpot. But in the first three months of this year almost 800 people with £1 in their accounts won prizes ranging from £25 to £100.

The odds of winning a prize with just £1 today stand at 34,000 to one, equivalent to an annual savings rate of 1pc. This is up from much shorter odds of 9,600 to one when Premium Bonds first started in 1957. Back then the top prize was worth £1,000 and the maximum a saver could hold was £500. Today the maximum stands at £50,000.

In 2020, NS&I worsened the odds of winning from 24,500 to one by reducing the number of prizes paid out.

The chance of winning is skewed in favour of those with the most bonds but around three quarters of all Premium Bonds holders – nearly 16 million people – have never won a single prize, figures previously obtained by Telegraph Money showed (see box above).

Savers must weigh up whether the gamble is worth it. The Bank of England raised central bank interest rates to 0.75pc this week. In theory this is good news for savers. But soaring costs mean no savings deals currently beat inflation, which stands at 5.5pc, its highest level for 30 years, and is forecast to rise further still.

Anna Bowes, of comparison website Savings Champion, said a dearth of deals had made Premium Bonds especially attractive but smaller bondholders with less chance of winning would become disillusioned as savings rates improved.

“The chances of winning big on Premium Bonds, no matter how small, has always been very attractive for savers. After rates on savings deals fell to next to nothing during the pandemic, when central bank rates hit a record low of 0.1pc, the lure became even greater still,” she said. 

“Unless the chances of winning increase again, savers may be pulled by increasingly higher rates on savings accounts, where they know the interest is guaranteed.” 

More than 21 million people own Premium Bonds, including children. Three million prizes are paid out each month, just two of which are worth £1m.

The average amount of money held in the accounts of former jackpot winners is £17,000. They sit through 60 draws over five years on average before taking home the £1m prize.

Three children under the age of 16 have won the jackpot.

Two million prizes worth a total of £73m have never been claimed, including one £100,000 unclaimed win.