The Society of Motor Manufacturers and Traders (SMMT) said production increased by 9.1% in August compared to the same period last year.
Output has risen by 12% so far this year to 1,132,727 units.
Demand for new cars is up at home and overseas, with a 10.2% uplift in exports driving growth.
Production for the domestic market increased by 6.2% last month to 27,804, while export volumes grew to 81,200.
In the year-to-date, more than 877,523 cars have been built for international customers - 13.3% more than in the same period last year, which the SMMT said demonstrated the ongoing international appeal of British-built vehicles.
Mike Hawes, SMMT chief executive, said: "August's strong performance is good news for car makers and welcome news for the UK economy, which depends on this thriving sector for an increasing share of UK exports.
"British car producers are exporting a diverse range of high quality, attractive new models that are in demand across the world thanks to multi billion pound investments made in UK plants over the past few years.
"Future success depends on continued investment in plant and products, and that in turn depends on the UK maintaining internationally competitive business and trading conditions."
Industry and Climate Change Minister Nick Hurd said: "With the Paris Motor Show taking place next week, today's figures are a powerful reminder of the strength of our automotive sector and the demand for British-made cars like the new Honda Civic, which is about to be exported across the globe.
"The automotive sector now accounts for a bigger share of our exports than ever before, and we will support this success by investing in innovation and continuing to give workers the skills they need to succeed."