It is the income (from the interest received on the savings accounts) that is important - not whether you have managed to save anything from that income after your living expenses. (if that was your question).
Savings accounts will normally have basic rate tax deducted from them, so you only ever see the net figure paid to you. If you have no other income (including pension income) you can apply to have the interest paid gross.
You need to add up all the GROSS income from your savings and see whether it is greater than your personal allowance against tax. This figure is �6475 this tax year for a person under 64. See here for figures for older people (the personal allowance is larger).
http://www.direct.gov.uk/en/MoneyTaxAndBenefit s/PensionsAndRetirement/MoneyInRetirement/DG_1 0023447