French-owned RCI Bank has upped the rate on its easy-access online Freedom account to 1.2% for both new and existing savers.
It puts it just behind Ulster Bank, which pays 1.25% on its e-Savings account.
With the Ulster Bank account savers are covered up to £85,000 if the bank runs into trouble by the Financial Services Compensation Scheme. With RCI Bank you have €100,000 (around £88,000) under the equivalent French scheme.
Other top online deals include Shawbrook Bank at 1.20%, Bank of Cyprus at 1.15% (including a bonus for the first year) and Ford Money at 1.07%.
On fixed-rate bonds the top rate for one year is 1.85% from Harrods Bank. OakNorth Bank pays 1.76% and Shawbrook, Paragon and Atom banks 1.75%.
Whereas, on tax-free cash Isas best rates come from Ford Money at 1% for both new and existing savers. Virgin Money pays 1.01% but limits you to three withdrawals a year.
The top one-year fixed cash Isa rate is Bank of Cyprus at 1.22% followed by Charter Savings Bank pays 1.21% and Paragon Bank at 1.2%.
For two years Charter Savings Bank pays a top 1.37% followed by Bank of Cyprus at 1.32% along with Virgin Money, Yorkshire Building Society and Progressive Building Society all at 1.3%.
How to beat inflation
To beat inflation, currently running at 2.6%, 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. We regularly keeps tabs on the savings market has found there are nine accounts that currently beat inflation.