This is the highest number of mortgage approvals since May 2010.
The total lending to individuals rose £0.4bn in June, lower than the previous six-month average increase of £1.2bn. The 12 month growth rate remained unchanged at 0.8%.
Samuel Tombs, economist at Capital Economics, said: "We doubt that the rise in the number of mortgage approvals in June marks the start of an upward trend in housing market activity.
“The bigger picture is that approvals have barely moved in recent months. What's more, survey measures, such as the new buyer enquires balance of the RICS Housing Market Survey, have recently pointed to approvals holding steady over the next few months.
Howard Archer, chief economist Eurozone & United Kingdom at IHS global insight, added: “Unsecured consumer credit remains very low compared to past norms. It is evident that consumer appetite for new taking on new borrowing remains limited while there is also an ongoing desire of many consumers to reduce their debt.
“Consumer desire to get a tighter grip on their finances is a reflection of current very low consumer confidence and is the consequence of an uncertain and somewhat worrying longer-term outlook for the economy and jobs as the major fiscal squeeze increasingly kicks in. Meanwhile, there remains limited availability of unsecured credit from banks.”
Peter Dixon, economist at Commerzbank AG, said: “It's all of a piece with the story that private sector lending, particularly with regard to the mortgage market, continues to contract. You can see that in both the lending secured on dwellings figures, which are down on the month and on the year. There is a lack of private sector liquidity demand there.
“The net consumer credit figures were marginally positive, but there doesn't appear to be a huge amount of credit demand out there.
“The money supply data reflects concerns about consumer deleveraging. Quantitative Easing was designed to boost monetary aggregates growth and, 15 months after the end of it, money supply is contracting again. So you can understand the arguments of those who want more QE, but as far as interest rates are concerned, it's clearly another argument for holding on and waiting and seeing.”