"Approvals for house purchase are broadly stable although remortgaging continues to rise as borrowers take advantage of cheap fixed-rate mortgages in particular."
Net lending is also higher than recent averages and is the highest monthly figure since March 2016.
Mortgage approvals for house purchase also rose slightly to 65,202, while approvals for remortgaging increased to 42,955 after falling to an eight-month low of 40,437 in April.
Annual growth in consumer credit remained strong at 10.3% in May, although below its peak in November 2016.
Jonathan Harris, director of mortgage broker Anderson Harris, said: "While there is likely to be considerable uncertainty ahead as a result of the ongoing Brexit negotiations, the mortgage market appears to be shrugging these off and steadily ticking along.
"Approvals for house purchase are broadly stable although remortgaging continues to rise as borrowers take advantage of cheap fixed-rate mortgages in particular. As speculation continues regarding the possibility of an interest rate rise, it may be that more borrowers are persuaded to take the plunge and secure a cheap deal before they miss out."
Jeremy Leaf, former RICS residential chairman, added: "These figures are interesting because they are not particularly interesting as they reflect what other surveys have been saying recently - that the market is fairly stable, showing no signs of particular change in the lead up to the general election. However, we would have hoped for higher numbers compared with this time last year, considering that the market then was still suffering following the introduction of the stamp duty surcharge."
