By Jon Sindreu And Jason Douglas 

LONDON--The British economy stepped up a gear in the second quarter, lifting growth prospects during the rest of the year but raising questions about how much longer the Bank of England can keep interest rates pegged at record lows.

The U.K. Office for National Statistics said Tuesday gross domestic product expanded 0.7% between April and June, an annualized rate of 2.8%. The figures are just a preliminary estimate, but they spell out that the economy has recovered from a slight slump in the first quarter--when quarterly growth was 0.4%--and is ready to gather pace during the remainder of the year.

Britain's pickup was driven by its powerhouse services sector, official data showed, which disappointed in the first quarter but now looks set to benefit from higher earnings and low inflation.

The industrial sector also posted a strong recovery, as the extraction industry in the North Sea came back to life after months of ultralow oil prices. Mining and quarrying activity picked up at the fastest pace in more than 25 years, the ONS said, aided by tax cuts for oil and gas producers set in March.

An increasingly buoyant economy could lead the Bank of England to bring forward its planned tightening of monetary policy. The BOE's policy interest rate has remained unchanged at a record-low 0.5% for more than six years, but officials have recently signaled the time to raise it--to keep medium-term inflation under control--is growing nearer.

Investors currently expect the U.K.'s central bank to nudge up interest rates early next year.

However, other indicators could muffle hawkish voices among BOE rate-setters, as official figures recently showed a small uptick in unemployment. In combination with strong GDP figures, this suggests the economy is being fueled by productivity gains instead of more people going into work. Labor productivity, which is the amount of output each worker produces in an hour, is a key gauge of economic health.

"A revival in productivity will help the recovery to achieve an above-trend pace over the coming quarters. What's more, this revival should help to keep inflation subdued," said Samuel Tombs, analyst at Capital Economics.

Stronger productivity would allow the Bank of England to keep monetary policy loose for longer, further boosting economic growth, because it would mean pay rises are translated into more goods and services being produced every hour--instead of prices going up.

Nevertheless, Tuesday's GDP figures also confirmed some of the ills that have affected the U.K. economy for a while. Manufacturers, which are having a challenging 2015, posted a slight fall in production during the second quarter. Recent surveys indicate factories continue to grapple with weak exports into the third quarter, hampered by the strength of the pound relative to other major currencies.

Official figures also showed construction output remained flat, although the ONS notes data for the sector is generally unreliable and prone to large revisions

Write to Jon Sindreu at jon.sindreu@wsj.com and Jason Douglas at jason.douglas@wsj.com