By David Milliken and Alistair Smout
The central bank also gave new guidance on when it might start to sell its 435 billion pounds ($574 billion) of British government bonds, saying this could come once rates have reached around 1.5 percent, compared with previous guidance of 2 percent.
Sterling rallied against the dollar on the news, heading for its biggest daily gain in two months. Short-dated bond yields jumped as markets priced in higher BoE rates.
"The likely timing of the next hike is less finely balanced than the markets expected. The surprising switch by BoE Chief Economist (Andy) Haldane to support an immediate rate hike puts August firmly on the table," Lloyds economist Jeavon Lolay said.
The BoE's Monetary Policy Committee voted 6-3 to keep rates at 0.5 percent, where they have been for most of the past decade, against widespread expectations in a Reuters poll for another 7-2 split.
The BoE raised rates in November for the first time since the financial crisis, and the central bank had looked ready for another increase in May, until the economy slowed in the first three months of 2018, due partly to bad weather.
Before Thursday's statement, most economists polled by Reuters expected rates to rise in August, but markets priced in a chance of under 50 percent and a majority of the public did not expect rates to rise at all this year.
Now, interest rate futures price in a two-thirds chance of an August rate rise, Societe Generale analyst Jason Simpson said.
Tightening in Britain, which leaves the European Union in March 2019, remains far more limited than in the United States, where the Federal Reserve plans to raise rates four times in total this year and three times in 2019.
ECONOMY "ON TRACK"
On Thursday, the MPC said their judgement that economic weakness would prove temporary appeared "broadly on track", and BoE staff confirmed a forecast that growth would resume what it sees as a sustainable rate of 0.4 percent in the second quarter.
Household spending and sentiment had bounced back strongly, and a sharp fall in factory output in April could reflect firms running down excess inventory which built up in the period of bad weather in the first quarter, the BoE said.
With unemployment at its lowest since 1975, the BoE says the economy is near full capacity, and interest rates will likely rise in a gradual and limited way over the next two to three years to curb inflation.
Haldane and the two other policymakers who voted to raise rates to 0.75 percent said recent wage deals and strong demand for workers raised the prospect of wages rising faster than the BoE forecast, and there was no reason to wait.
However, many economists remained wary about the chances of an August rate rise, burnt after the apparent certainty of a May rate rise evaporated in the space of a few days in April, following weak data and dovish remarks by BoE Governor Mark Carney.
"The MPC has repeatedly talked up the chances of rate hikes, only to disappoint when all the data don't fall into place. We still struggle to see how the data will warrant a hike in August," said Samuel Tombs of Pantheon Macroeconomics.
At the end of last year Britain's was the slowest-growing economy among the G7 group of rich nations, as businesses held back from investing ahead of Brexit and high inflation triggered by the 2016 referendum eroded households' disposable incomes.
Inflation has fallen slightly faster than expected from a five-year high of 3.1 percent in November, though the BoE said on Thursday it expected it to rise in the short term due to a weaker pound and higher oil prices.
Haldane has a reputation for wide-ranging interests and thinking that does not always represent the mainstream at the BoE, so it remains to be seen if other BoE officials follow his lead on monetary policy.
Carney is due to give a major speech in London this evening, when he will have ample chance to set out his own views.
(Additional reporting by Andy Bruce; Writing by David Milliken; Editing by Andrew Roche)
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