Rates for new savers from banks and building societies continue to edge up. The top deal on easy-access accounts comes from French-owned RCI Bank, part of the Renault group, at 1.65% before tax (1.32% after tax) on its Freedom account.But here you are not covered by the UK compensation scheme. If the bank goes bust you claim from the European scheme where the maximum amount is €100,000 (around £73,500).Just behind come Tesco Bank Internet Saver on 1.6% (1.28%) and BM Savings, part of Halifax, with the same rate on its Online Extra account. But both come with a bonus payable for the first year you are in the account - after which you will have to move your money or suffer a low rate.Kent Reliance's new Easy Access account pays 1.45% (1.16%), and Paragon Bank's Limited Easy Access 1.46% (1.17%). Neither deal is boosted by a short-term bonus.On fixed-rate deals internet bank Charter Savings has edged its rate up to a top 2.07% (1.66%) for one year. RCI Bank pays 2.05% (1.65%) and Shawbrook Bank 2.05% (1.64%).For two years you can earn 2.4% (1.92%) with Paragon Bank, 2.35% (1.88%) with RCI, or 2.32% (1.86%) with Charter Savings Bank.On fixed-rate cash Isas, Virgin Money has upped its rate to 1.76% for one year, while Shawbrook Bank now pays a top 1.85%. For two years Virgin Money pays a top 2.06%.On easy access cash Isas the best deal is 1.51% from Post Office Online Isa, including a bonus for the first year. Virgin Money matches this rate but you are limited to three withdrawals a year. The top deal with no bonus or withdrawal restrictions is 1.4% from Nationwide.