There was a seven per cent month-on-month rise in mortgage lending in August, CML said, with the total amount borrowed reaching £22.5bn.
Lending was up 15 per cent annually, up from £19.5bn in August last year - the highest figure for August since 2007.
CML senior economist Mohammad Jamei said:
Widely-voiced fears in recent months about the housing market have proved to be wide of the mark.
Prospects for house purchase activity post-referendum look slightly subdued, when compared to late 2015 and early 2016. However, sentiment in the market recovered in August. This is reflected in stronger-than-expected transaction figures, and in our gross lending estimate.
The figures from the CML come after data from Rightmove showed house prices rebounded in September. Asking prices were up 0.7 per cent month-on-month, according to the property portal, with prices on properties with two bedrooms or less increasing by 3.3 per cent on last month.
Other parts of the economy have also proved resilient to the shock of the Brexit vote; the Office for National Statistics recently said that retail sales held up well in August, after a bumper month in July, and the West End's retail sales have been booming on the fall in the pound.
House prices after Brexit: a short history
- In June, RICS predicted house prices would drop for the first time since 2012
- Rightmove report house prices fell by 0.2 per cent in June
- Brexit vote, everyone wants to know what will happen to house prices, so we asked the experts
- FTSE 100-listed housebuilder shares take a tumble
- Data from Halifax shows house prices fell after the Brexit vote
- Mortgage approvals fell to an 18-month low in July
- Nationwide reports house prices went up again in August