They are increasingly turning to investment funds, investment trusts or structured products to boost their returns, even though these investments can put their capital at risk.
Analysis by HSBC shows that savers who put money into fixed rate accounts four or five years ago are facing a "savings precipice" this year when they come to reinvest.
Rates on similar best buy accounts are nearly 2% lower on four-year fixed-term accounts and 1.32% lower for five-year terms.
Average interest rates on four and five-year fixed-rate bonds are now 3.73% and 3.95%, according to Moneyfacts, and that's before tax is taken off.
By contrast, after-tax returns of 4% and more are available on investment funds and investment trusts.
Although the capital value of funds and investment trusts can go down when stock markets fall, the income they pay to investors, which comes from company dividends, can rise over time as companies increase their dividend payouts.
In order to take advantage of higher levels of income available from shares and corporate bonds, investors are becoming more prepared to see their capital fluctuate in value.
Jeffrey Deans of Glasgow-based independent financial advisers Save & Invest says that income investors are becoming less averse to risk.
He said: "People are beginning to take the view that they will keep about 20% of their savings in cash accounts for emergencies but they are prepared to take a risk with their remaining capital because they need the extra income."
A similar trend has been seen by Derek Stewart at independent financial advisers Strategic Asset Management in Glasgow.
He said: "I find more investors are shifting towards prioritising income over family inheritance and are prepared to accept some capital depreciation."
However, he argues that the risk to an investor's capital can be reduced by spreading it across a diversified portfolio of investment funds, consisting of a mixture of stock market and corporate bond funds, which invest in fixed interest securities.
His firm recommends a "balanced income, balanced risk" portfolio of funds that provides an estimated yield of 4.6%. Funds in the portfolio include Invesco Perpetual High Income, Schroder Income Maximiser, M&G Strategic Corporate Bond and Newton Global Higher Income.
Advisers suggest that other income products may also be used in the mix.
Colin Campbell, director of financial planning at Innovate Financial Services in Edinburgh, says that, alongside corporate bonds and equity income funds, his firm would consider structured products, such as the Investec FTSE 100 Bonus Income Plan 24, which pays an annual income of 6%, and can be held within an ISA so that the income is tax free.
These plans usually run for a fixed term of five or six years. The problem with these is that, while they aim to provide the original capital back at the end of the term, the outcome depends on the performance of the FTSE 100 Share Index.
If it falls more than 50% during the term and does not recover, then investors will lose some of their money.
Jeffrey Deans says he is now including investment trusts, such as Edinburgh Investment Trust and Temple Bar, among his recommendations for investors seeking income.
These are currently yielding 4.3% and 4% respectively after basic rate tax. He points out that investment trusts have the advantage of being able to smooth out their income payments, if necessary using reserves built up in the good years as they are able to retain up to 15% of the income they receive each year.
Advisers believe investors seeking income are more willing to consider stock market-related investments because they are accepting the ups and downs in the market.
However, Mr Stewart suggests that if investors are concerned about passing on their savings to the next generation, they could consider using the extra income they have gained to take out an insurance policy, which pays out a lump sum when they die and write it in trust for their children.
Savers who really don't want any volatility need to take maximum advantage of cash ISAs so that they receive the interest free of tax. A number of fixed rate ISAs offer monthly interest options, such as those offered by BM Savings, which currently pays up to 4.12% over a five-year term or Saga, which offers 3.64% over three years.