The figures released by the Society of Motor Manufacturers and Traders (SMMT) show this was an increase of 6.3% on 2014. The previous record was set at 2.58 million in 2003.
Last month also broke the record for December sales, an increase of 8.4% on the previous year at 180,077.
SMMT chief executive Mike Hawes said high consumer confidence, wage growth and 'l ow-interest' finance deals have encouraged motorists to buy new cars.
The fourth consecutive year of growth means sales have exceeded their pre-recession levels after dipping below two million in both 2009 and 2011.
Some 43 consecutive months of growth in year-on-year sales ended in October, but this was followed by a 3.8% rise in November and a bumper December.
Mr Hawes said he has "every reason to expect the market to hold broadly steady in 2016."
In the wake of the diesel emissions scandal, Volkswagen car sales fell by 0.4% in December compared with the same month in 2014. The brand experienced a 20% decrease in registrations in November.
For the year as a whole Volkswagen sales were up by 4.2% compared with 2014.
There were mixed results for other VW brands last month, with Seat down by 46.4% but Audi up by 14.1% and Skoda by 4.2%.
The 2015 market share of all diesel cars fell from 50.1% to 48.5%.
Hawes said: "There has been a lot of comment and concern around air quality and diesel.
"I think the fact that the market for diesel has held up demonstrates that, for a lot of consumers, they are still driven by fuel economy and diesel offers better fuel economy."
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