The figures from the Society for Motor Manufacturers and Traders (SMMT) come days after Japanese car maker Nissan said it was no longer planning to build new X-Trail models at its car plant in Sunderland.
Annual figures for 2018 showed new car sales fell 7% over the year - the second year in a row of declines and the biggest fall since 2008.
The latest SMMT data, for January 2019, showed 161,013 vehicles left forecourts last month, down from 163,615 a year earlier.
It was the fifth consecutive month of decline and was driven by a slump in demand for diesel cars - down 20% - continued to lead the decline, while petrol car sales were up 7%.
There was also an overall increase in sales to private owners, after a fall in December - but there were downturns in the business and fleet buyer market.
Demand for alternatively-fuelled vehicles such as hybrid and electric cars rose 26%.
SMMT chief executive Mike Hawes said: "To restore momentum, we need supportive policies, not least on vehicle taxation, to encourage buyers to invest in new, cleaner vehicles that best suit their driving needs - from the latest petrols and diesels to an ever growing range of exciting electrified vehicles."
The figures come after the SMMT recently issued a "red alert" over Brexit, as production and investment in the car industry tumble ahead of a possible no-deal scenario.