Coventry BS and Paragon Bank have both launched online easy-access accounts paying 1.25 per cent.
They sit among the best buys, just behind RCI Bank and Kent Reliance, both at 1.3 per cent, and Bank of Cyprus UK, at 1.31 per cent.
With Bank of Cyprus UK, the rate includes an initial bonus only payable for the first year. After that, the rate drops to 0.85 per cent.
Coventry BS and Paragon Bank have both launched online easy-access accounts paying 1.25 per cent. They sit among the best buys, just behind RCI Bank and Kent Reliance
The other accounts have no bonus and, unlike some top-paying accounts, there are no restrictions on how often you can take money out of your account each year.
Paragon Bank has also launched an easy-access cash Isa at 1.25 per cent, a top rate matched by Coventry BS and Shawbrook Bank.
Nationwide paid a higher 1.3 per cent, but closed the accounts to new savers at the start of this month.
Fixed-rate cash Isas pay slightly more, with a top one-year rate of 1.48 per cent from Kent Reliance, followed by 1.45 per cent from Ford Money.
The rates on offer on fixed-rate cash Isas fall far short of those available on bonds.
The top rate for one year here is 1.9 per cent from Investec Bank or 1.85 per cent from Kent Reliance.
Basic-rate taxpayers can earn their first £1,000 of interest in a taxable account each year without paying any tax. Higher-rate taxpayers get a £500 allowance.