In total, 40,281 new homes were registered - 30,691 in the private sector and 9,590 in the public sector - compared to 34,163 (24,428 private sector; 9,735 public sector) in the first quarter of 2014.
This represents a year-on-year 26% increase for the private sector, with the public sector marginally down by 1%.
Figures for March show that 17,210 new houses were registered (12,699 private sector; 4,511 public sector), an increase of 32% registered in the same month last year (13,068; 9,051 private sector; 4,017 public sector).
NHBC chief executive Mike Quinton said: "Our figures show an encouraging start to 2015 with new housing registrations up 18% on the first quarter of last year. Housing growth levels remain strong across virtually every part of the UK.
“However, we have made clear that the UK is still building way below the volumes of homes that we need. NHBC looks forward to working with government to ensure that high quality new housing is a top priority.”