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Output rose 0.4 percent compared with 0.3 percent growth in the quarter to June, the Office for National Statistics said on Wednesday. A Reuters poll of economists had forecast 0.3 percent.
Sterling hit a day's high against the dollar on the figures, while British government bond and share prices fell as financial markets further adjusted to the prospect of higher interest rates.
Britain performed much better than most economists expected immediately after last year's vote to leave the European Union, and was one of the fastest-growing major advanced economies in 2016.
But it slipped to the bottom of the pack earlier this year, posting its worst first-half performance since 2012 at a time when its peers have enjoyed robust growth.
Scotiabank economist Alan Clarke called the latest 0.4 percent growth figure "hardly a boom... merely in line with potential".
Nevertheless, "it removes the last hurdle standing in the way of a rate hike at next week's meeting," he said.
A Reuters poll published on Tuesday showed the BoE is widely expected to raise rates to 0.50 percent from 0.25 percent on Nov. 2, due to concerns that the economy cannot grow as fast as it used to without generating excess inflation.
Last month the BoE said Wednesday's preliminary data was likely to show 0.3 percent growth, though it might be stronger due to improving consumer demand.
FOCUS ON PRODUCTIVITY
A further argument in favour of higher rates might come from solid bank lending figures from industry association UK Finance.
The ONS data showed the vast services industry was behind the bulk of Britain's economic expansion in the third quarter, but manufacturing also contributed, helped by a rebound in car production.
The reading will also be a small boost for under-pressure finance minister Philip Hammond ahead of his annual budget on Nov. 22. He has limited room for manoeuvre because of Britain's poor productivity performance.
"My focus now, and going into the budget, is on boosting productivity so that we can deliver higher-wage jobs and a better standard of living," he said in a statement after the data.
In year-on-year terms, third-quarter growth was unchanged at 1.5 percent, also slightly stronger than analysts had expected.
Britain's dominant services sector grew by 0.4 percent in the third quarter, maintaining its momentum from the previous quarter, the ONS said. Industrial output expanded 1.0 percent, its fastest growth in more than a year.
Construction continued to struggle, however, contracting by 0.7 percent on the quarter - its sharpest fall since the third quarter of 2012.
The preliminary estimates of GDP do not include a breakdown of spending, and are heavily based on estimated data.