Gross lending totalled an estimated £11.3bn in May, up from £10.1bn lent in April and 1% higher than in May 2010.
The increase represents a bounce back after a 14% drop in April blamed on the Royal Wedding and Easter holidays.
The data includes lending for both house purchase and remortgage.
Despite a modest pick-up in overall lending activity during May, lending for house purchase is running below year earlier levels – as April Bank of England approvals data indicate.
Looking ahead, interest in remortgaging is now also likely to be less pronounced, as expectations of higher interest rates this year recede.
The Monetary Policy Committee once again kept rates unchanged at its June meeting – for the 27th successive month.
Michael Coogan, director general of the CML, says: “Gross mortgage lending in May recovered after low activity levels in April.
“Distorting effects from Easter and bank holidays cloud the current picture, but the likelihood seems to be for essentially flat levels of lending over the next couple of months.”