Under the new ‘super’ ISA rules, savers can hold the full amount in cash. Currently, a maximum of £5,760 can be in cash.

“The impact this will have on people looking for ways to make the most of their savings will be huge with people now able to put in £15,000 a year with much greater flexibility,” said Nationwide’s Chief Executive, Graham Beale.

While some savers may be tempted to take advantage of the higher cash allowance – and we may even see a proliferation of temporary bonus rates to tempt savers in – interest rates on cash ISAs remain at paltry levels and inflation is quietly eroding savings.

Jafar Hassan, personal finance expert at uSwitch.com, said: “With interest rates at an all-time low, anyone who does save the full amount only stands to gain an extra £25 or so in tax free savings.

As a result, fund groups have been urging people to consider putting more of their money into stocks and shares ISAs.

Tom Stevenson, investment director at Fidelity Worldwide Investment, said: “We would urge savers to consider if their savings are working hard enough to meet their goals. Those stuck in low-paying cash ISAs should consider that equities could provide much greater potential for long-term growth and income.”

In fact, Fidelity calculated that savvy savers could become ‘ISA millionaires’ within 25 years following the changes to ISA limits.

Under the old rules, a saver investing their full ISA allowance each year – starting with this year’s allowance of £11,520 – and assuming a 5 per cent annual return, would take 29 years to grow their ISA pot to £1m.

But as a result of yesterday’s changes, savers who use their full £15,000 ISA limit could be ISA millionaires – with all returns sheltered from the tax man – in their 25th year of investing. This assumes an investment of £11,880 (the 2014/15 ISA limit from April until July) in April 2014, with a top up of £3,120 in July 2014 when the new £15,000 limit is in place.

Stevenson recommended that ISA investors looking to take advantage of boosted limits should start early, save as much as they can afford and resist the temptation to stick with the safety of cash.

He explained: “Many of us first assume that cash is the safest option when it comes to investing our savings. While this is partly true – you won’t get the ups and downs in cash savings that you might with stock market, and cash is ‘liquid’ so you can access it more flexibly – leaving your money in cash risks big erosions to your savings pot over time. With interest rates at record lows, the returns on high street cash savings are extremely limited.”

Fidelity estimates that if a saver had invested £15,000 into stocks and shares from the end of March 2014 to 28 February, they would be £18,635 better off than someone who instead held the same amount of cash in an average UK savings account.

However, more flexible transfer rules between stocks and cash could ease the burden on families looking to build a secure cushion in their personal finances, perhaps for use as an emergency fund.

Julie Hutchison, family finance expert at Standard Life, said: “The higher limit will make it easier to build an appropriate cash fund as an emergency buffer, then consider making the most of the potential offered by a stocks and shares ISA, which can be the smart next step to take for the longer term.”