This growth was boosted by the buoyant services and manufacturing industries, which are continuing to go from strength-to-strength.
Shilen Shah, Bond Strategist at Investec Wealth & Investment, said: "Third quarter UK GDP accelerated to 0.4%, above the consensus figure of 0.3%, with some indications that the dominant services sector continues to be in expansionary territory".
However, 0.4 percent is a still below the U.K.'s long-term growth rate, as data suggest 2017 could be the poorest growth year for the British economy since the financial crisis in 2007-2008.
Services remained the largest contributor to overall growth, and the sector's output increased 0.4% in the quarter - the same rate as in Q2 - driven by IT services, motor trades and retail.
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The figures come just over a week before the Bank of England makes a decision whether to raise rates.
This raises the prospect of an interest rate rise when the Bank of England meets on 2 November.
"However, construction output fell for the second consecutive quarter, although it remains above its pre-downturn peak".
The pound was up 0.36% per cent against the U.S. dollar to £1.3179 and 0.27% against the Euro to £1.1188 on Tuesday morning as news of the UK's better than expected growth broke.
The Chancellor, Philip Hammond, said of the performance: "We have a successful and resilient economy which is supporting a record number of people in employment".
According to the ONS, the figures bring the estimated full year growth to 1.5% - meaning that the economy is expanding at a slower rate than in 2016, which stood at an annualised rate of 1.8%.
UK GDP grows by 0.4% quarter-on-quarter but rising inflation seems to be squeezing household spending.
"Yet if rates do rise as expected, the move will be largely symbolic - though it will be the first rise in over 10 years".
Inflation in the United Kingdom has jumped to a five-and-a-half year high at 3%, while wage growth remains subdued. That trend would likely reverse if the BoE increases in the base rate back to its previous level.