Initial returns from car sales examined by the SMMT suggest as many as 420,000 units will be sold this month, compared with the previous record of 408,024 in March last year.
Estimates suggest that up to £6 billion worth of new cars will have left showrooms by the end of the month, as consumer and fleet confidence remain high.
SMMT chief executive Christopher Macgowan said: 'The strength of the market demonstrates the competitive nature of UK franchised dealers. The manufacturers' aim of supplying increasingly cleaner, safer and better specified cars is paying dividends to all.
'This is not the industry blowing its own trumpet here - buyers are doing it for us.'
The prediction of a record March, on top of two very strong sales months at the start of the year, were backed by the Retail Motor Industry Federation.
Alan Pulham, franchised dealer director of the RMI, said: 'The high February sales show that consumers still prefer buying from franchised dealers.
'Although the specification of many cars has improved, most manufacturers have kept prices static.'