Against the dollar, the pound rose as much as 0.9 percent to hit a day's high of $1.4015 after trading flat before the BoE announcement, in which the bank also voted to keep rates unchanged. It traded at $1.3955 1225 GMT.
Against the euro, sterling rallied more than 1 percent to hit a one-week high of 87.41 pence.
Britain's internationally exposed FTSE 100 hit its session low, down 1.1 percent, after the BoE decision.
Sterling has been one of the best performing currencies this year, hitting its highest levels since before the vote in June 2016 to leave the European Union, but the rally has come to an end in recent sessions with the pound slipping.
With rising inflation expectations globally, investors are predicting central banks could tighten policy faster, but the outlook for Britain has been overshadowed by the state of UK-EU talks for Britain's exit from the trading bloc next year.
The Monetary Policy Committee raised interest rates for the first time in a decade in November.
In its announcement on Thursday, the BoE said rates probably needed to rise sooner and by a bit more than it thought in November, after it raised its economic growth forecasts for Britain due to the strong global recovery.
"This is a Brexit-contingent hawkish signal," said Viraj Patel, and FX analyst at ING in London. "The comment in itself was the surprise. That was a clear message from the bank that the (interest rate) curve was a little too flat for their liking."
With the BoE's comments contingent on a smooth exit from the EU, which Britain is due to leave next year, analysts said further sterling gains above $1.40 were likely to be limited until there was clarity on a transition deal in the coming months.
Sterling hit a 16-month high of $1.4346 in January before falling back. It remains up more than 3.4 percent against the dollar this year but below the plus $1.50 levels since before the vote to exit the EU.
In bond markets, British two-year government bond yields rose to the highest since December 2015, rising by around 6 basis points after the decision to 0.706 percent.
Interest rate futures now show a 60 percent chance of a BoE rate hike in June, and it is fully priced in for the August meeting, according to interest rate futures markets.
Before Thursday's statement, investors saw a nearly 50-50 chance of the next hike coming in May.