There were 47,312 approvals last month, up from 44,124 in June.
However, this was still less than the monthly average of nearly 51,000 approvals recorded in the previous six months.
Ashley Brown, director of the independent mortgage broker Moneysprite, said: "July's numbers may be better than June's but they're lower than the previous six-month average for both remortgages and house purchases. That's a far more accurate portrayal of where the market is at.
"The month-on-month numbers jump up and down but the overall trend is one of extremely low borrowing levels and a market that's flatlining.
"Even though the Bank of England's Funding for Lending scheme is making more credit available, the LTV apartheid continues.
"There is no shortage of lenders offering low LTV products, and competition has driven down rates.
"But at the higher LTV end of the market it's a different story. The products are there, but interest rates are dramatically higher and the deposit requirements are prohibitive.
"This excessive caution is having a severe chilling effect on the market, with thousands of homeowners who'd like to move unable to do so.
"Until this changes, expect the market to bump along at its current uninspired levels."
