Nationwide said savers should be able to choose to put all of their annual Isa allowance into cash Isas, which it argued would encourage people to save more and help would-be home buyers to build up larger sums of tax-free cash towards a deposit.
Britain's biggest building society is urging the Government to use next month's Budget to double the amount that hard-pressed savers can place into cash Isas.
At present, savers can only place half of their Isa allowance into cash savings and the remainder must be invested in stocks and shares. Changing the rules would mean that people could put £11,280 into a cash Isa during this financial year, instead of the current limit of £5,640.
Nationwide said that just under half of people who are eligible for an Isa actually have one, with around £390 billion currently held in cash and stocks and shares Isas across the UK. It argued that raising the cash Isa limit would give people greater flexibility and enable those approaching retirement to move more of their savings into cash to give themselves more certainty over their returns.
Savers have struggled to make any real cash out of their nest eggs amid nearly four years of the Bank of England base rate being held at a record low.
Savings rates have plummeted further in recent months following the introduction of a Government scheme which has given lenders access to cheap finance to help borrowers. Analysts have said that the Funding for Lending scheme has made lenders less concerned about needing to attract savers' deposits.
Richard Marriott, head of savings at Nationwide, said that raising the cash Isa limit would "send out the right message to all of Britain's savers, that it is worth saving, no matter how much or how little". He said: "With many first-time buyers struggling to raise a deposit and with pensioners relying more on their savings income, we believe this is the right time for the Government to act on Isas."
To add further complications for savers, financial information website Moneyfacts has also warned that it is becoming increasingly difficult for Isa holders to move all of their previous savings into a new top-paying account.
Many savers have traditionally viewed Isas as one-year products and they have regularly switched where their money is held when a bonus period ends in order to make sure they keep getting the best returns for their cash. However, just three of the top-paying variable cash Isas allow savers to transfer money in from older Isa pots, compared with nine out of 10 two years ago.
Moneyfacts said savers could end up having to leave some cash stuck in old accounts paying poor rates. Sylvia Waycot, editor of Moneyfacts, said: "Whilst this current trend remains, savers need to find an Isa that not only pays a great rate but also from a provider that they are comfortable doing business with for longer than 12 months."