There were a record 1,420,636 new cars registered in the first half of 2016 - an increase of 3.2 per cent on last year.
This works out at around 350 new cars being bought every hour for 24 hours a day.
Part of this growth has been driven by an increase in the number of people buying hybrids and electric cars, with sales of eco-friendly motors up 21.3 per cent.
But June saw a decline of 0.8 per cent in sales, dropping from 257,817 to 255,766.
The Ford Fiesta was once again the biggest selling car of the month, with 11,357 registered. Ford has now sold 68,833 Fiestas this year - 61 per cent more than second place, the Vauxhall Corsa.
The Corsa was the second-biggest seller of June (8,837), with the Ford Focus (6,833), Volkswagen Golf (6,775) and Mini (6,284) making up the top five.
Mike Hawes, the Society of Motor Manufacturers & Traders’ chief executive, said: “It is far too soon to determine whether the referendum result has had an impact on the new car market.
“The first six months saw strong demand at record levels but the market undoubtedly cooled over the second quarter.
“It is important government takes every measure to restore business and economic confidence to avoid the market contracting in the coming months.”