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Charlie Bean suggested it was likely to reach that level between 2017 and 2019.
The rate has been at the historic low of 0.5% since March 2009 and the Bank’s governor has indicated it will not start rising before next spring.
But Mr Bean told BBC Radio 4’s The World This Weekend there were economic advantages to beginning earlier.
Mr Bean is a member of the Bank of England’s Monetary Policy Committee, which sets interest rates.
Charles Bean is a member of the committee which sets UK interest rates
The UK interest rate fell to 0.5% in the wake of the worldwide financial crisis in 2008. It has been kept at that level amid concerns that the finances of many individuals and businesses remain too weak to withstand a rise.
But recent worries about rising house prices in parts of the UK and evidence that the economy is strengthening have intensified the debate over when rates might start to increase.
“The bank rate averaged about 5% in the decade or so before the crisis,” Mr Bean told the BBC.
“It’s reasonable to think that given the headwinds that are still out there as well as some the global forces that perhaps the level that we go to three or five years out might a couple of percentage points below that,” he said.
At the last meeting of the Bank of England’s Monetary Policy Committee (MPC) on 7-8 May, members appeared to be shifting their opinions towards raising interest rates.
However, notes from the meeting showed that they voted unanimously to keep rates at a record low of 0.5%.
Mr Bean said: “There’s a case for moving gradually because we won’t be quite certain about the impact of tightening the bank rate given everything that has happened to the economy.
“It might not operate in quite the same way as before the crisis. So that’s an argument if you like for being a bit cautious, moving in baby steps to avoid making mistakes.
“If you want to pursue that strategy you need to start taking those baby steps a bit earlier, otherwise you end up being behind the curve.”
Economist and former government adviser Will Hutton explained why the Bank was being so cautious: “Typical mortgage payments could double over the next three years.
“If you look in the financial pages, you’ll see that you can fix your mortgage for 2% for two years or 3% for five years. In three years’ time those rates will double.”
Mr Bean also voiced concern that financial markets were being complacent, failing to factor in risks to the global economy, from instability in the Ukraine to rate rises in the US.
Source: BBC News