"The judgment as to when to apply the next interest rate is the key call," Carr told CNBC at the World Economic Forum in Davos, Switzerland on Wednesday. Economic and political policymakers, as well as corporate executives, attend the annual meeting.
"I think the approach he (Bank of England Chief Mark Carney) is going to take is to watch and wait and act correctly, rather get railroaded into a quick decision."
The Bank of England has held rates at record lows of 0.5 percent since March 2009.
Governor Mark Carney has said he will not consider raising rates until U.K. unemployment falls to 7 percent, which he originally forecast would not happen before the end of 2016.
However, data in the last few months has suggested the U.K. economic recovery is accelerating.
In particular, official statistics showed on Wednesday that unemployment fell to 7.1 percent in the three months to November — a whisker away from the central bank's targeted level.
(Read more: UK unemployment lowest since early 2009)
"The U.K. is having a very strong run," said Carr. "But these things have to be cared for and husbanded and if we lean back too much, the risk is, these things will slide."
The Bank of England's Court of Directors is responsible for managing its affairs outside of formulating monetary policy.