"Mortgage lenders stayed calm, rates stayed low and many lenders looked to build market share with competitive deals."
The figure is also 3% higher than the £20.1 billion lent in June last year.
Gross mortgage lending for the second quarter of 2016 was therefore as estimated £56.1 billion - 10% lower than Q1 but 8% higher than the second quarter of 2015.
CML senior economist, Mohammad Jamei, said: "The result of the EU referendum is likely to affect the housing market, but there remains considerable uncertainty. Although mortgage firms have ample lending capacity, activity levels are likely to bear the brunt of any market adjustment over the next six months or so, as buyers and sellers wait to get a clearer idea of where we might be headed.
"But as with the economy, the UK housing market’s starting position is relatively favourable, with transactions having increased by almost 80% from post-crisis lows. Over the next six months, activity is likely to soften modestly, while lending will be driven more by remortgaging and less by house purchases.
"We also expect some form of monetary easing to be undertaken by the Monetary Policy Committee when it meets on 4 August, given the uncertain outlook that has set in after the vote result."
Henry Woodcock, principal mortgage consultant at IRESS, added: “It may have been a surprise to some that gross lending was up in May by 4% and now the momentum has continued into June, rising a considerable 16% from May to £20.7 billion.
“The positive indicators were there if one looked beyond the rhetoric of the daily bombardment of contradicting referendum messages. Mortgage lenders stayed calm, rates stayed low and many lenders looked to build market share with competitive deals.
“One month on from the leave vote, rates are predicted to stay low for another two years. Investment in the mortgage market continues with new lenders such as Atom Bank and others coming to market in the next six to 18 months.
“We could continue to see an increase in lending over the coming months, but the longer term lending outlook remains a bit ‘foggy’. The EU exit decision came as a surprise to many and a lot will now depend on how things settle following the initial jolt. The consultancy Centre for Economics and Business Research has suggested a construction slowdown may be on the horizon – which will only exacerbate the housing crisis and could lead to fewer affordable houses being built.
“We are in uncharted waters making things very hard to predict with any amount of certainty.”
