There were 45,940 loan approvals for house purchase worth £6.4bn in May, up 3.2% by value from the 45,447 approvals worth £6.2bn in April.
However, the number of approvals was slightly lower than the previous six-month average of 45,957.
The number of approvals for remortgaging also increased slightly by number, up from 28,074 in April to 28,759 in May, but by value remortgage activity remained static at £3.6bn.
The research also shows that lending secured on dwellings rose by £1.1bn in May, slightly higher than the previous six-month average increase of £0.8bn.
That represents a monthly increase of 0.1% and an annual rise of 0.7%.