Definitely don't close your ISA if you're a taxpayer. If you can afford to keep it going for the long term, you may value the tax break if taxes subsequently rise. It's better to look around and try to find an ISA provider offering a better interest rate. If you want to move your ISA to another provider, you have to request a transfer form from your provider and let the process be handled directly between the existing and the new provider. If you withdraw the money, you effectively close your ISA and lose its tax free status.