Almost 1.6 million cars were built in the UK in 2015, an increase of 3.9% over the previous year, reported the Society of Motor Manufacturers and Traders (SMMT).
Nearly four out of five cars were exported, up by 2.7% on 2014, despite a huge fall in sales to China and Russia.
Exports to Russia slumped by 69% and by 37% to China, where the economy has been slowing.
But this was offset by economic recovery in Europe, where demand for UK-built cars increased by 11% in 2015.
The region now accounts for 57.5% of all UK car exports. SMMT chief executive Mike Hawes said membership of the European Union was "vital" for the automotive sector.
Production of the MINI increased by 12.4% last year to 201,000, Toyota by 10.4% (190,000), Vauxhall by 9.5% 85,000) and Jaguar Land Rover by 9% (489,000), while Nissan recorded a 4.7% reduction (476,000) and Honda was down by 2% (119,000), said the SMMT.
The United States overtook China as the biggest export destination, with demand up by a quarter last year, while health growth was also reported in Australia (53%), South Korea (55%), Turkey (41%) and Japan (35%).
Hawes said: "Despite export challenges in some key markets such as Russia and China, foreign demand for British-built cars has been strong, reaching record export levels in the past year.
"Achieving these hard fought for results is down to vital investment in the sector, world class engineering and a committed and skilled UK workforce - one of the most productive in the world.
"Continued growth in an intensely competitive global marketplace is far from guaranteed, however, and depends heavily on global economic conditions and political stability.
"Europe is our biggest trading partner and the UK's membership of the European Union is vital for the automotive sector in order to secure future growth and jobs."
Chancellor George Osborne said: "Backing Britain's car industry has been a priority for this government and today we see the industry going from strength to strength.
"I am hugely encouraged that manufacturing is at a 10-year high and exports are at a record level. All this means jobs and the security of a pay packet for workers and their families.
"Our plans to rebalance the economy mean we have to continue to build on our great manufacturing strengths in the Midlands and the North of England, and work together to ensure that Britain continues to prosper as a global leader in car production."