The trade body reported that house purchase approvals in May were up a quarter on the same point last year and said these schemes were likely to stimulate further rises in coming months.
Remortgaging also jumped 17% compared to 2012 figures, continuing a rising trend across this year.
The BBA said that gross mortgage lending from its members hit £8.6bn in May, 7.5% higher than the recent levels, and that the average house purchase approval rose to £159,200.
Jonathan Harris, director of mortgage broker Anderson Harris, said: “The mortgage market continues to improve with borrowers attracted by lower rates and easing criteria. Help to Buy is already helping first-time buyers and is expected to give a further boost to this group, as well as second steppers, from January when the guarantee element of the scheme is rolled out.
“While lending volumes are improving, we remain some way off a sustained recovery in the housing market as caution continues to prevail. However, mortgage brokers and estate agents are still reporting a high level of enquiries so we expect this to continue to feed through to improved official figures in coming months.”
Jonathan Samuels, CEO of Dragonfly Property Finance, added: “Encouragingly, while people are more active on the mortgage front, they are proving conservative about taking on other forms of debt.
“More people are now taking out mortgages but they are doing so much more responsibly. They are aware of the pressure other debts can place on their finances.
“If the property market is to have any kind of stability moving forward then there is still a need for consumers to deleverage.
“UK households are still carrying a huge amount of debt and that needs to be paid down before the property market can recover in earnest.”