BBA members approved 43,265 mortgages for house purchases in June, up from 41,881 in May and 13.5 percent higher compared to a year ago.

Tighter rules on mortgage lending, requiring banks to check more closely that borrowers will be able to afford loan repayments when interest rates go up, took effect in April. Further rules were introduced in late June.

"These figures show that mortgage approvals are rising again," said Richard Woolhouse, chief economist at the BBA. "That's encouraging because those decisions are a leading indicator of what's happening in the housing market."

"But the jury is still out on exactly how the new rules are affecting customer applications or approvals."

The Bank of England imposed its first limits on how much most people can borrow to buy a home only in late June.

The measures were in response to Britain's rapidly recovering housing market. House prices are growing at more than 11 percent annually, according to one measure.

However, the BoE said on Wednesday that there were signs of a modest slowing in Britain's economy, most evidently in the housing market.

The BBA data does not include lending by building societies, which are included in separate Bank of England data next due for release on July 29.

(Reporting by Ana Nicolaci da Costa; Editing by Catherine Evans)