Some savings rates have started to edge up, with Kent Reliance now paying a top 2.1% before tax (1.61% after tax) fixed for one year.
The next best deal is 1.95% (1.56%) from Investec Bank.
Kent Reliance is also raising its two-year deal to a top 2.3% (1.84%). Investec Bank also pays 2.3% (1.84%) for two years.
On easy-access accounts West Bromwich has a new WebSaver Limited Access launching today (29 July) at 1.4% (1.12%), but you are limited to three free withdrawals a year.
BM Savings new Online Extra 12 pays 1.31% (1.05%), including a bonus but with no withdrawal restrictions.
The rate drops to 0.5% (0.4%) once you have been in the account for a year. Best deals with no bonus and no withdrawal restrictions come from Virgin Money Easy Access and Sainsbury's Bank e-Saver, both at 1.3% (1.04%).
The top easy-access tax-free cash Isa rate is 1.6% from Cheshire and Derbyshire building societies, but you cannot transfer your existing cash Isas into these accounts.
For transfers you can earn 1.55% with BM Savings Extra Isa 11. But the rate includes a bonus and drops to 0.5% after you have been in the account for 12 months.
Kent Reliance also pays 1.55% and the rate is not boosted by a bonus. Other good deals with no bonus include Nationwide Instant Isa Saver and Virgin Money Easy Access Cash Isa, both at 1.5%.
West Bromwich Building Society is raising the rate on its WebSaver Isa to 1.5% for new and existing savers on 1 August.
On fixed-rate cash Isas, top rates include 1.75% from Kent Reliance and 1.65% from Tesco Bank, both fixed for one year. For two years you can earn 2.1% with Kent Reliance or 2.05% with Nationwide.
This article was written for our sister website Money Observer