The rate increases show how competitive the savings market has become since the Bank of England increased the base rate to 4.25% last month.

However, both accounts can be beaten elsewhere. Santander pays 4% on its Santander Edge Saver, but you need a Santander Edge current account to be eligible. Yorkshire Building Society pays 3.6% on its Rainy Day savings accounts.

Chip increased the rate on its instant access account from 3.4% to 3.55%. It had previously introduced the rate of 3.4% AER in mid-March.

Simon Rabin, CEO of Chip, said: “The latest rise – only three weeks since we hit an industry high since 2009 with 3.40% – highlights our commitment to always keeping the rate on our Chip instant access account highly competitive. It might not always be so far ahead of all the alternatives like it is now, but we aim to keep the rate pretty damned amazing.”

Top up from Tandem

Tandem launched an interest rate ‘top up’ for its instant access savings accounts in January. Under the top up scheme, Tandem customers are invited to apply the rate to their instant access savings account – adding an increased rate on top of their existing rate, which will apply for 12 months.

The underlying interest rate on Tandem’s instant access savings account is 3.15% AER / 3.11% gross (variable). The available top up is now 0.35%, bringing the total interest rate to 3.50% AER / 3.45% gross (variable). Interest is calculated daily and paid monthly into the account.

Both the underlying interest rate and the top up are variable, meaning Tandem can change it at any time. It says it may increase the underlying interest rate or top up with immediate effect and inform customers afterwards. But if it decides to reduce the underlying interest rate or top up, it will give customers at least 30 days’ notice before the change comes into effect.

Applying the top up doesn’t change the underlying instant access savings account and customers will still have instant access to their money. They won’t need to go through the account opening process again, and will automatically get any changes to the top up rate if they’re inside their top up period.

Once their top up period has come to an end, if there’s a top up being offered at the time, customers will be able to add the new top up to their account. Existing customers who chose not to add the top up will still remain on their existing rate.