The supermarket unveiled the deal, which is open to both new and existing customers, on 2 February. It said daily applications last week were in the tens of thousands.

The high interest paying account guarantees 3% on balances up to £3,000 and boosts Clubcard rewards.

Tesco Bank promised the variable interest rate would not fall below 3% for two years from April.

There are no minimum direct debit, standing order or monthly pay in requirements and customers can open two current accounts, doubling the benefits.

The bank has not revealed exactly when applications will re-open but expects sign-ups to open again in the coming weeks.

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A Tesco Bank spokesperson said: “Last week we launched our new guarantee for Tesco Bank Current Account customers. It gives our customers certainty on the level of interest their accounts will earn, as well as even more Clubcard points when they shop at Tesco.

“The feedback from our customers has been brilliant. We are also delighted by the unprecedented demand from new customers applying to take out accounts with us.

“In order to best serve our existing customers, today we have decided to pause accepting new applications for the time being. In the coming weeks, we will let customers know when they can apply again for the Tesco Bank current account.”