In recent months banks have ramped up efforts to tempt new customers and rates have topped 8 per cent. But to date such accounts have not paid great returns on larger balances.

Alliance & Leicester’s Premier Direct account, for example, pays 8.5 per cent but only on balances up to £2,500, for a year.

Lloyds’ approach however means the bigger the balance, the higher the interest paid. It also promises it is “not a short-term promotional offer”.

Sean Gardner of price-comparison service Money­Expert.com said the account was an “innovative addition” to the market but the rates “aren’t exactly exceptional” below £5,000.

“Any of the 179 instant access accounts that pay more than 5 per cent must be worth considering if you’re in the market for a high-interest account with easy access to cash,” Gardner added.

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