Savers can now earn 1.26% in the new top easy-access account from internet-based Charter Savings Bank.
The new deal puts it just ahead of Ulster Bank at 1.25%.
ICICI Bank UK Hi-Save Bonus Account also pays 1.25% but the rate includes a 0.6% bonus payable until 30 September next year.
On fixed rate bonds Metro Bank has upped the rate on its one-year deal to a top 1.95%, available online or through its branches.
Cash Isa rates are also edging up with the Charter Savings Bank Easy Access Cash Isa (Issue 5) at 1.1% for new savers.
Savings accounts to beat inflation
To beat inflation compromises need to be made as all of the small number of regular savings accounts that pay more than inflation require savers to have a current account with the provider.
Moneywise keeps tabs on the savings market has found there are nine accounts that currently beat inflation.
This article was written for our sister magazine Money Observer.