If we’re still talking about banks that provide current accounts, I don’t think there is.
Of banks that provides current accounts, I think Barclays and Virgin Money currently offer the best rates on easy access savings accounts with a whopping 0.50%.
Some banks do provide decent rates on limited amounts of money within their current accounts (e.g. Nationwide Flexdirect, 2% on up to £1,500, for up to 1 year,