NatWest customers can access its Digital Regular Saver account which pays 6.17 percent on between £1 and £150 a month, up to an overall maximum of £5,000.

Halifax Regular Saver pays a fixed rate of 5.5 percent and on deposits of between £25 and £250 a month.

TSB Regular Saver also offers its current account holders a high interest monthly savings account, paying five percent for one year on between £25 and £250 a month. “You can access the money whenever you wish,” O’Brien said. 

After one year the money is automatically switched into TSB’s variable rate Easy Saver account, which pays a much lower rate of 0.9 percent. After one year, that falls to 0.8 percent.

For savers who want instant access to their money, O'Brien highlights Barclays Rainy Day Saver. “This pays 5.12 percent on balances up to £5,000, but only if you are a member of Barclays Blue Rewards.”

Customers can manage the account using the Barclays app, online banking but O’Brien said: “If you have more money to save there might be better options.”

Virgin Money customers with a Private Current Account or Current Account Tracker can open its Private Savings Account, which has a variable rate starting from 4.25 percent and offers no-notice withdrawals..

App-based Chip is currently offering an instant access account which is open to anyone at 3.71 percent. “You can save up to £250,000 and access the money at any time.” 

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