Fixed-rate deals are falling with several banks closing their top-paying accounts to new savers.
The best one-year deal comes from RCI Bank at 2.06 per cent before tax (1.65 per cent after).
With this French-owned bank your money is covered by the European compensation scheme, which gives €100,000 (around £74,500), rather than the UK scheme.
Paragon Bank pays 2.01 per cent (1.61 per cent) and Aldermore Bank 2 per cent (1.6 per cent).
For two years the best deal is 2.35 per cent (1.88 per cent) with RCI Bank, or 2.25 per cent (1.8 per cent) with Close Brothers.
Easy access accounts
On easy-access accounts you can earn 1.65 per cent (1.32 per cent) at best from internet accounts run by both RCI and ICICI banks.
Virgin Money pays 1.41 per cent (1.3 per cent) both online and in the high street, but you are restricted to making three withdrawals a year from your account.
On easy access cash Isas Coventry Building Society pays a top 1.5 per cent, while Virgin Money has relaunched its Defined Access Isa at 1.41 per cent. It limits you to three withdrawals a year.
The best one-year fixed rate cash Isa comes from Tesco Bank with a tax-free 1.75 per cent, followed by Virgin Money, Shawbrook Bank and Leeds Building Society all at 1.65 per cent.
For two years the top rates is 2 per cent from State Bank of India (UK), while Leeds Building Society pays 1.9 per cent.