Gross interest is the sum of interest a saver will receive before the deduction of tax, and net interest is the sum of interest a saver will receive after the deduction of tax
Update (2016): Prior to April 2016, banks and building societies charged interest of 20% on savings income, and to receive gross interest -- some individuals on a low income and certain organisations were exempt and could receive gross interest -- a R85 form had to be completed. The R85 form has now been withdrawn, but can still be read about at the following webpage: https://www.gov.uk/government/publications/income-tax-getting-your-interest-without-tax-taken-off-r85. Since April 2016, all savings income paid by banks and building societies is gross interest, and any tax that is due on savings income -- for high earners -- is dealt with through the PAYE system or self assessment system. You may be asking why the policy change: due to the historically low Bank of England base rate, the interest offered by banks and building societies on savings has decreased massively (compared to prior decades) and the tax generated for the Her Majesty's Treasury (HM Treasury) -- also referred to as the Exchequer -- has also decreased in relation. Therefore, the UK government probably felt it a good political move, to 'throw a bone' to hard pressed savers, and one which will have a minimal impact on the Exchequer.
Older content (2013): At present, March 2013, savings income has a 20% income tax deduction -- interest with a 20% income tax deduction is referred to as net interest, and interest without a 20% income tax deduction is referred to as gross interest. A 20% income tax deduction is causing major problems for savers due to savings accounts currently paying such a low rate of -- due to a low Bank of England base rate and quantitative easing. Savers are finding it nearly impossible to beat the rate of inflation -- CPI or RPI in the UK -- when receiving gross interest, let alone net interest. At present, the UK Gov website states that for 2012-2013, to receive tax-free savings, a saver must earn less than the following: Under 65 - £8,105; 65 to 74 - £10,500; 75 or older - £10,660. Banks will provide an application form at their branch or online -- if you are eligible for gross interest -- and will take no longer than 10 minutes to fill out. For more information on tax-free savings, visit the following link: https://www.gov.uk/apply-tax-free-interest-on-savings