LONDON—Registrations of new cars in the U.K. rose to their highest level in nine years in the first half of this year, beating industry expectations as the British economy continues to rebound strongly after the financial crisis.

New car registrations, which closely mirror sales, rose 6.2% in June to 228,291 units taking the number for the first half of 2014 to 1.29 million, up nearly 11% from the same period a year earlier, the U.K….