The change follows the Chancellor’s announcement in the Budget that NS&I – the organisation that issues premium bonds – would help support savers.

In addition, the number of £1m prize draws will double from the August draw.

Each pound invested in premium bonds is individually entered into a monthly prize draw. The increased limit means anyone investing an additional £10,000 will have 10,000 more chances to win.

According to NS&I, the total amount invested in premium bonds, which are guaranteed by the Treasury, has risen from £19.7bn in 2003 to £45.7bn today – an increase of 131 per cent.

More than 21 million people are said to hold these bonds.

Julian Hynd, retail director at National Savings and Investment (NS&I), said: “Premium bonds are one of the nation’s favourite ways to save. Raising the maximum amount that can be invested is good news for customers because the more they invest, the greater their chance of winning a tax-free prize.”

According to Hargreaves Lansdown, premium bonds can be a valuable tool for higher rate taxpayers who have already used their ISA allowance and want a secure home for some of their cash.

The chance of winning £1m tax-free could be appealing, particularly since many taxed savings schemes have interest rates below inflation.

Danny Cox of Hargreaves Lansdown said: “The increased investment limit is likely to appeal to wealthier pensioner investors, as will the doubling of the £1m pay-out to two. The Pensioner Bond launching at the beginning of 2015 will have broader appeal and to be relevant to more the millions of retired investors with only modest sums to invest.”

A further increase of the investment limit to £50,000 is expected in 2015-16.