In a letter to customers, Natwest which is owned by RBS, said: “Global interest rates remain at very low levels and in some markets are currently negative. Dependent on future market conditions, this could result in us charging interest on credit balances.”

According to BBC News, if the bank implements the change, it will become the first UK bank to introduce negative interest rates.

Personal banking customers would not be affected by the move.

Bank of England governor Mark Carney has strongly hinted that interest rates could be cut at some point over the summer, as the EU referendum result has led to a deterioration of the UK’s economic outlook.

Markets were bracing themselves for a reduction in the bank base rate earlier this month, but the Bank of England’s Monetary Policy Committee decided to keep rates at 0.5%, the same level since March 2009.

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An RBS spokesperson said: “We will consider any necessary action in the event of the Bank of England Base Rate falling below zero, but will do our utmost to protect our customers from any impacts. We have no current plans to pass negative rates through to personal or business customers.”

A recent poll conducted by Mortgage Solutions shows that mortgage brokers are divided on the direction of interest rates next month. Half expect rates to hold at 0.5%, while 43% expect a reduction in the base rate of 0.25%. The remainder predict an increase of 0.25% or more or a reduction of 0.5% or more.

Most MPC members expect monetary policy to be ‘loosened’ in August, according to the committee’s latest minutes, with the exact extent of any measures from a rate cut to quantitative easing based on its updated forecast next month.