The third consecutive month of increased truck demand means the year to date figures are up by 41% on the same period last year.
Van registrations in March were topped by the 2.5- to 3.5-tonne sector, which rose by almost 24%.
Mike Hawes, SMMT chief executive, describes it as a "strong first quarter performance yet again", adding: "In the van and truck markets, there has been a clear shift towards the larger vehicles in the sector in the first three months of the year.
"Both 2.5-3.5 tonne vans and 3-axle artic trucks have seen a sharp increase in registrations as operators seek to make their fleets as flexible and cost effective as possible."
Ford says its March CV sales were the highest on record, at 16,497 units. Reflecting the wider industry figures, Ford's CV registrations were up by 43% for the first quarter of 2015.
Mark Ovenden, chairman and managing director of Ford of Britain, says it is "a stellar sales performance".