No.
Your savings comprise capital and income. Say you put £10,000 on deposit and it earned you £500 a year. The one is capital and the other income.
Either way, the £500 isn't going to be taxed as your income is below the tax personal allowance plus there is a tax free personal savings allowance of £1,000 p.a for basic rate taxpayers (£500 for higher rate).
In accounting terms, cash in a bank account is capital. Moving it about does not constitute income.