LONDON (Reuters) - Britain’s economy appears to be picking up speed, according to a survey on Friday that will reassure the Bank of England a day after it raised interest rates for the first time a decade.

Sterling hit a day’s high against the dollar after the IHS Markit/CIPS services Purchasing Managers’ Index (PMI) jumped to 55.6 in October from 53.6 in September, its biggest one-month rise since August 2016.

Despite nervousness among businesses about Brexit, the reading was its highest since April and exceeded all forecasts in a Reuters poll of economists.

The survey of services businesses, which account for around 80 percent of British economic output, follows relatively upbeat PMI readings this week for the smaller manufacturing and construction sectors.

Taken together they suggest the economy is growing at a quarterly rate of 0.5 percent, IHS Markit said, picking up from growth of 0.4 percent in the three months to September.

Britain’s economy has lagged behind others in Europe and beyond this year as sterling’s plunge following last year’s vote to leave the European Union pushes up inflation and uncertainty over the shape of Brexit causes businesses invest more slowly.

“The UK PMI may be starting to show some convergence with its firm global counterpart,” JPMorgan economist Allan Monks said.

Growth in the services sector outpaced that in the euro zone, as measured by a flash estimate, for the first time since January, the PMI showed. IHS Markit will publish a final estimate for the euro zone on Monday.

“The Bank of England will likely see October’s (PMIs) as supportive to the decision to raise interest rates,” said Howard Archer, chief economic adviser to the EY ITEM Club consultancy.

A general view of the Canary Wharf financial district in London, Britain October 24, 2017. REUTERS/Kevin Coombs

Many private economists had warned before Thursday’s decision by the Bank that a rate hike would be premature.

“However, serious uncertainties over the outlook evident among services companies fuels suspicion that it is likely to be some considerable time before the Bank of England hikes interest rates again,” Archer said.

The BoE raised rates for the first time in more than 10 years on Thursday and said its next increases would be “very gradual”.

Deputy Governor Ben Broadbent said on Friday that the Bank’s signal that it may need to raise interest rates two more times to bring down inflation was not a promise.

Businesses are unsure about the outlook, and optimism among services companies remained well below its long-run average, fuelled mainly by uncertainty over Brexit, the PMI data showed.

“A deeper dive into the numbers highlights the fragility of the economy,” said Chris Williamson, chief business economist at IHS Markit, which compiles the PMIs.

BoE Governor Mark Carney said on Thursday that the central bank’s next move would be heavily influenced by the progress of talks on Britain’s departure from the EU.

Growth could get a boost if a transitional deal gave businesses confidence to invest.

But a failure to reach a deal would further weaken the pound and intensify inflation pressure.

The services PMI, which covers non-retail businesses, said firms were putting up prices at the fastest rate since April.

Costs increased rapidly, though at the slowest rate in just over a year, possibly tallying with the Bank’s view that the inflationary effect of last year’s more than 10 percent fall in the value of the pound is starting to fade.

Across the economy as a whole, the PMI showed that job creation was at its weakest since March.

“Squeezed margins and concerns about the economic outlook had led to more cautious hiring strategies,” IHS Markit said.

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