The number of mortgage approvals in October was 27% higher than a year ago, with remortgaging up 34% and house purchases up 21%.
However the BBA said that bank lending to companies is polarised. There is growth in lending to wholesale, retail and manufacturing sectors, while lending to the construction and real estate sectors is continuing to contract.
Net capital market finance has grown by £18.2bn in 2015 so far, with larger companies using that as an alternative to loans and overdrafts.
Richard Woolhouse, chief economist at the BBA, said: “These statistics show that housing market activity remained strong in October, with gross mortgage borrowing 26% higher than a year ago and at its highest level for seven years.
"Consumers remain confident and their incomes are growing. Mortgage rates are at multi-year lows and people are snapping up the very competitive deals being offered by banks."
Meanwhile figures published today by the Council of Mortgage Lenders showed the recovery was fairly balanced across the UK.
First-time buyers took out 3,700 loans in Wales - up 16% on the previous quarter and on Q3 2013 - borrowing £410m which was up 21% on the previous quarter and the same quarter last year.
There were 3,900 home-mover loans in the third quarter, up 8% on the previous quarter and 3% more than in quarter three 2014. The total value of these loans was £550m, up 12% on the second quarter and up 6% on the third quarter 2014.
Remortgage lending in the quarter in Wales grew quarter-on-quarter and year-on-year by volume and by value.
In Scotland there were 8,500 first-time buyer loans - 4% up on the previous quarter and 16% up on Q3 2014. First-time buyers in the period borrowed £920m - up 2% on the previous quarter and 16% on Q3 2014.
At 10,000 loans, there were 12% more homemover loans in the third quarter than the second, and 15% more than in Q3 2014. The value of homemover lending was £1.5bn, up 16% on the second quarter and 17% up on the third quarter 2014.
Remortgage lending went up in value quarter-on-quarter and year-on-year.
In Northern Ireland meanwhile homeowner house purchase activity increased to 3,600 loans - up 16% on the second quarter and 6% on the third quarter in 2014.
First-time buyers and home movers saw similar trends to each other with both increasing quarter-on-quarter and year-on-year.
The number of loans for remortgage remained the same quarter-on-quarter at 1,700 loans, but up 55% in volume compared to the third quarter 2014.
And in greater London first-time buyer loans totalled 12,800 in London - up 17% on the previous quarter but down 1% on the third quarter in 2014. First-time buyers borrowed £3.4bn - up 24% on the previous quarter and 4% on the same quarter in 2014.
There were 10,800 home-mover loans in London, up 32% on the previous quarter and 5% on the third quarter of 2014. The total value of these loans was £4bn, up 38% on the second quarter and 11% on the third quarter 2013.
Remortgage lending increased 8% by volume and 10% by value compared to quarter two. Compared to the third quarter last year, it was up 15% by volume and 25% by value.
Paul Smee, director general of the CML, said: “Borrowers appear to be taking advantage of relatively favourable economic conditions and this could mean a continual upward trajectory moving into the new year.”
