The BBA attributed the drop to the implementation of the Mortgage Market Review.
However despite regulatory changes gross mortgage borrowing still remains significantly higher (26%) than it was last year.
Richard Woolhouse, chief economist at the BBA, said: “Our figures indicate that the heat appears to be coming out of the housing market.
“These are the first mortgage approval figures we have seen since the introduction of the Mortgage Market Review, so it is significant they have fallen for the fourth month in a row.
“This is being driven by a drop in remortgaging and people borrowing against the value of their homes.”
The statistics also revealed a boost in business lending in May which was bolstered by borrowing from the energy sector.