There was no change to the annual rate of growth which remained at 1.5%, beating market expectations of a dip to 1.4%.
Manufacturing also boosted the headline GDP figure after improving from a weak second quarter.
"However, the importance of "programming" to our economy is not the whole story".
This beat economists' forecasts for a 0.3% rise, and was largely thanks to growth in the business services and finance sector, which expanded by 0.6% in the three months to September.
That caused the pound to jump nearly 1 per cent against the dollar to $1.326, while it was 0.6 per cent up versus the euro at €1.123.
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The Q3 outturn was slightly firmer than the average rate of growth seen in H1 2017 (0.3%), which may give some ammunition to those on the Bank of England's MPC who are leaning towards vote for a rise in interest rates in their November meeting.
Ben Brettell, senior economist at Hargreaves Lansdown, said: "A slightly improved performance from the United Kingdom economy in Q3, with output growing by 0.4%".
The UK economy grew faster than expected in the third quarter, according to the first estimate released by the ONS this morning.
A rate rise is seen as a negative for stock markets, which have grown fat from almost a decade of cheap money from central banks, however most believe Bank of England Governor Mark Carney will now be forced to hike at the Bank's next meeting on 2 November.
Laith Khalaf, Senior Analyst at Hargreaves Lansdown, said this morning that "markets are now pricing in an 80% chance of a rate rise next week, but the central bank has disappointed on this score before". Following recent hawkish comments from the MPC, markets were already regarding a return to 0.5% as a near-certainty. For the commercial real estate industry, higher interest rates and rising inflation make borrowing and construction more expensive for owners, which can have a constraining effect on the market but can also lead to an increase in property prices. That trend would likely reverse if the BoE increases in the base rate back to its previous level. "I expect the Bank to proceed with caution from here".