Official figures showed that services output expanded by 0.4% in the first month after Brexit driven by rising retail sales, a robust performance from the film industry and computer programming.
The update came as the Office for National Statistics (ONS) revised its reading for the UK economy, with gross domestic product (GDP) growing 0.7% in the second quarter, up from a previous estimate of 0.6% for the period.
The ONS said the revision was triggered by a better performance from services and investment in the three months to June.
Darren Morgan, head of GDP at the ONS, said the fresh data shows there is "no sign of an immediate shock to the economy" from the EU referendum result.
He said: "Despite some very weak indicators appearing in the immediate aftermath of the referendum, estimates gathered by the ONS from more than 23,000 firms now suggest that the services sector, which accounts for three quarters of the economy - in fact grew strongly in July.
"Further information also suggest that the whole economy also grew slightly more strongly in the months before polling day than previously thought."
Howard Archer, chief UK and European economist at IHS Global Insight, said the buoyant result from the services sector provides a "significant boost" to the UK economy's third quarter growth prospects.
He said: "The economy has shown resilience so far in the aftermath of June's Brexit vote, helped significantly by consumers' willingness to keep on spending amid still decent fundamentals, and the weakened pound lifting foreign orders for UK goods and services.
"This resilience has helped consumer (especially) and business confidence rebound from their July lows."
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