This stability in lending is underpinned by more optimistic expectations of growth in the economy.
HM Treasury now expects GDP growth of 1.3% this year and 2.1% next which are respectively 0.4% and 0.5% higher than three months ago.
CML chief economist Bob Pannell said: "We are beginning to experience a healthy and broad-based recovery in mortgage lending activity.
"We attribute much of this turnaround to the improvement in funding markets generally and also to the Funding for Lending Scheme.
"The Bank of England’s approvals data suggests that the positive tone for house purchase and remortgage lending will continue.”
Pannell said the talk of a housing boom was a tell-tale sign that the market was beginning to recover.
He added: “But as we have argued elsewhere the housing market recovery to date appears fairly unexceptional in nature at least compared with that of the early-mid 1990s.”
Sophie Hall, head of intermediaries at Avelo, said the levelling out of lending represented a pause for breath rather than an end to the recent signs of recovery.
She said: In reality first-time buyers are still flocking to the market in their droves. A combination of rock-bottom rates caused by Funding for Lending and the added assistance of Help to Buy will see demand go from strength to strength in the latter part of 2013.”
Jonathan Harris, director of mortgage broker Anderson Harris, saw the stability as “extremely encouraging” because it suggested a sustained recovery rather than creation of a housing price bubble.
He said: “The economy is turning a corner but let's not get too carried away there is still a long way to go. The danger of over-reaction to a house-price bubble is that any confidence in the market is extinguished just as it is establishing itself. Lending volumes and house prices are still well below pre-crisis levels.”
Mark Dyason, director of independent UK mortgage broker Edinburgh Mortgage Advice, added:"While August was much the same as July this shouldn't be mistaken for a lack of momentum. The average mortgage broker continues to be exceptionally busy and demand is rampant.
"While the property market is improving across the UK as a whole prices, with the exception of London and certain areas of the South East, are still relatively affordable. That is adding to the demand."
David Brown, commercial director of LSL Property Services, said: “The only real area of concern is house building where there is a prominent shortfall. To keep house price rises sustainable the government needs to do everything possible to encourage and assist the construction industry to build more homes, ensuring supply keeps pace with demand.”
And Jeremy Duncombe, director, Legal & General Mortgage Club, said: "Increased lending figures seem to confirm that confidence has well and truly taken root in the mortgage market.
"Helped by Government stimulus, consumers and lenders are more optimistic about the state of economy and it is encouraging to see this reflected in mortgage lending.
"That said there is still work to be done. An increased supply of affordable housing and more innovation when it comes to mortgage products will bring a healthier balance to the market and encourage this fledgling recovery into something stable and longer lasting.”
