The number of
mortgages approved for house purchase hit a 13-month high in May.
The British Bankers' Association said 31,162 loans were approved for people buying a property during the month, 7% more than in April.
The figure was also 16% higher than it had been in May 2008, the first time the annual measure has shown an increase since November.
But the ongoing weakness in the remortgage market dragged down the overall lending figures, with total advances of £7.7bn the lowest since February 2001.
Net lending, which strips out redemptions and repayments, also fell for the third month in a row to £2.3bn, a level last seen in early 2001, when the average mortgage taken out for house purchase was just £74,400, compared with £133,600 in May.
The number of loans arranged by people remortgaging fell further during May to a near-nine-and-a-half-year low of just 24,847, 60% below levels seen 12 months ago.
BBA statistics director David Dooks said: "Steady monthly increases since last November have seen the number of loans approved for house purchase recover to levels seen in early 2008, although gross and net mortgage lending show a subdued wider mortgage picture.
"However, unlike much of the mortgage market, the high street banks are still seeing lending growth and improved mortgage availability is reflected in higher average loan approval values."