During the month, 61,760 mortgages were approved - just over a thousand more than in January.
It was the third month in a row that approvals have risen, and the highest figure since August 2014.
Even though the rise was small, economists said it indicated that the housing market had bottomed out, and was now facing a steady improvement.
Nevertheless the number of approvals is still well below the recent peak of 75,453 in January 2014.
"Housing market weakness has bottomed out, and activity is now gradually turning around," said Howard Archer, chief UK economist with IHS Global Insight.
Last week the Nationwide reported that annual house price inflation had fallen from 5.7% in February to 5.1% in March.
The number of mortgages being granted across the UK hit a six-month high in February, Bank of England data shows.