The top one-year rate is 1.65% from Tesco Bank and Aldermore Bank, while Halifax pays 1.55%. The best two-year deal comes from Nationwide at 2.05%.
On easy access cash ISAs you can earn 1.55% with BM Savings including a bonus for the first year, after which the rate drops to 0.5%. Virgin Money pays 1.5% with no bonus.
Both accept transfers in from the cash ISA savings you have already built up.
Cheshire and Derbyshire BS pay a slightly higher 1.6%, but they are only available through their branches and you can only put in this year's cash ISA allowance.
On taxable easy access accounts the best deal comes from Sainsbury's Bank e-Saver Special at 1.35% before tax (1.08% after basic rate tax) with no strings attached and no bonus boosting the initial rate.
West Bromwich Building Society Websaver Limited Access pays a slightly higher 1.4% (1.12%) but you are limited to making just three withdrawals a year.
On taxable bonds Investec pays 1.95% (1.56%) and Paragon Bank 1.9% (1.52%). For two years you can earn 2.35% (1.88%) with Aldermore Bank.