Some 203,585 cars were registered last month, which is the most in May since 2002, the Society of Motor Manufacturers and Traders (SMMT) said.
Demand for diesel cars grew 5%, while petrol models saw a small decline of 0.6%.
Uptake of alternatively fuelled vehicles increased by 12.1%.
Some 1,164,870 cars have been registered in 2016 so far, up 4.1% on the same period last year.
But May was the second consecutive month of sub-3% growth, demonstrating that the market is stabilising following a record 2015.
Mike Hawes, SMMT chief executive, said: "The new car market in May remained high with compelling offers available on the latest vehicles, but the low growth is further evidence of the market cooling in the face of concerns around economic and political stability.
"Whether this is the result of some buyers holding off until the current uncertainty is resolved or a sign of a more stable market for new cars remains to be seen."
Year on year, Volkswagen car sales saw a 7.3% slide as the German manufacturer continued to suffer as a result of the diesel emissions scandal.
The brand had 16,050 registrations in May, compared with 17,316 in the same month in 2015.
Its year-to-date sales for 2016 are 6.3% down on the same point last year.
Volkswagen Group admitted last September that 482,000 of its diesel vehicles in the US were fitted with defeat device software to switch engines to a cleaner mode when they were being tested for emissions.
The Wolfsburg-based company announced that 11 million vehicles were affected worldwide - including almost 1.2 million in the UK.
Other VW brands had mixed results in April.
Year-on-year sales for Audi were up 1.2% and Skoda rose by 4.1%, but Seat was down 23.9%.