Some 37,200 approvals for house purchase worth £5.7 billion got the green light in July, slightly down on a 17-month high of 37,337 the previous month, the British Bankers' Association (BBA) reported.
The BBA said the "stronger pattern" seen in the mortgage market since the start of the year has continued into the summer months.
Mortgage approvals to home buyers are almost a third (31%) higher than in the same period last year and remortgaging approvals are more than a third (40%) higher.
However, overall mortgage lending remains "subdued" because home owners are making high repayments on their loans, the BBA said.
The low interest rate environment and various Government schemes to boost the housing market mean several mortgage lenders have been offering their lowest ever rates in recent months.
With poor returns generally on offer on savings, this has made it more attractive for people to use any spare cash to pay down their mortgage debt.
Schemes such as Funding for Lending and Help to Buy have prompted stronger competition, making mortgage deals easier to access.
Lenders, estate agents and property websites have been reporting a pick-up in activity in recent months as more first-time buyers flood into the market.
Jonathan Harris, director of mortgage broker Anderson Harris, said that despite the uplift in activity, house sales are still "far lower than they were at the height of the boom years".
But he added: "Mortgage brokers and estate agents are still reporting a high level of enquiries and we expect these to continue to feed through to improved official figures in coming months."
The BBA said people put £8 billion on credit cards in new spending in July, which was higher than the recent monthly average and in line with stronger retail sales.
However, a general mood of consumer caution continued and repayments on credit cards outweighed new spending, with £8.1 billion paid back during the month.
Banks are seeing a general trend of people turning to their plastic to finance their spending. As people become more reliant on their credit cards, personal loan and overdraft borrowing is shrinking.
There was also a fall in total business borrowing levels in July and annual growth continues to contract.
Net borrowing by non-financial businesses decreased by £3.3 billion in July, while for financial businesses it decreased by £3.9 billion.
The BBA said smaller businesses are funding expansion through savings while larger firms are accessing equity and bond market funding.