Interest rates have climbed to 0.5% percent - for the first time in a decade.
Customers have enjoyed record low rates since 2007, staying at 0.25%.
The cost of borrowing will now rise, meaning loans and mortgages will face a hike.
A BoE rate hike would follow the pattern set by the U.S. Federal Reserve and to an extent by the European Central Bank, which has said it will start to scale back its stimulus plan.
Those economies are motoring ahead, however, and Britain's planned departure from the EU in March 2019 makes its future harder to predict.
Most economists polled by Reuters said the BoE should wait for clearer evidence that higher wages will keep inflation above its 2 percent target once the effect of last year's post-Brexit-vote fall in the pound fades.
"It would probably be more sensible to wait," said Seamus Mac Gorain, a former BoE economist who is now a fund manager at JP Morgan Asset Management, which controls $476 billion of fixed income assets such as government bonds.
Raising rates to 0.5 percent will not derail the economy. But further increases might be damaging, he said.
"If it ends up being a policy error, it will only be because they make a larger change in rates."
Underlining that risk, a survey on Thursday showed optimism in British construction firms - a bellwether of the wider economy - now stands at it lowest level since late 2012, around the last time Britain flirted with recession.
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