If your income is less than £15,600 a year you may be entitled to tax free savings interest. You can reclaim the bank interest tax already paid If you didn't pay tax overall because your income was below the personal allowance before the 6th April 2015 or if you qualify for the tax free savings interest after 6th April 2015.
Personal allowance ye 5 April 2015 (standard) £10,000
Personal allowance ye 5 April 2016 (standard) £10,600
Tax Free Savings Interest £5,000 ye 5 April 2016 (in addition to your personal allowance) .
If you were born before 6 April 1938 or if you get Blind Person's Allowance, Marriage Allowance or Married Couples Allowance it can be more.
To reclaim the overpaid tax you must fill in form R40 (found on our links page) and send it to HM Revenue and Customs (HMRC). You must reclaim within 4 years of the end of the relevant tax year.