Lloyds Banking Group grew its net lending to UK businesses and households through the Funding for Lending Scheme (FLS) by £3.1 billion in the third quarter of 2013. This was the biggest increase of any participant in the scheme.
Royal Bank of Scotland's lending turned positive, at £245 million, after a drop in the second quarter.
The Bank of England lauded the scheme's contribution to the pick-up in the economy but warned that lending to small businesses remained subdued.
Paul Fisher, executive director for markets at the Bank of England, said: "An economic recovery has taken hold.
"These data show that a significant improvement in credit conditions, aided by the FLS, is now feeding through to lending.
"But credit supply to businesses remains relatively subdued, especially to SMEs (small and medium-sized enterprises)."
The Government launched FLS to help lift the economy out of recession.
Cheap funds were made available to banks and building societies to lend to UK households and businesses.
Bank of England Governor Mark Carney recently announced the scheme will be refocused on encouraging lending to businesses amid concerns about the housing market heating up.
A Lloyds spokesman said: "We have committed more than £28 billion of gross new lending to UK businesses and homebuyers since we launched our discounted FLS offers in September 2012.
"We have continued to grow our lending to SMEs by 5% year-on-year, on a net basis, and we have already exceeded our pledge to lend £6.5bn to first time buyers in 2013."
The Bank of England said net lending by banks was £5.8bn in the three months to the end of September, three times the £1.6bn of the previous quarter. Lending had fallen in the two quarters before that.
Matthew Fell, the Confederation of British Industry's director for competitive markets, said: "Despite overall FLS lending substantially increasing, Bank of England data shows that net lending to SMEs continues to fall so the recent move recalibrating the scheme towards business lending is welcome."
British Bankers' Association chief economist Richard Woolhouse insisted that small businesses are borrowing more in gross terms.
Nationwide was the second biggest lender under FLS, providing a net £2.7bn in the quarter. Santander UK showed the biggest drop in net lending of £2.1bn.
Lloyds confirmed that Lord Blackwell will succeed Sir Win Bischoff as its chairman from April 3.
Asked if the former head of the Prime Minister's Policy Unit will be replaced as chairman of Lloyds' insurance arm Scottish Widows, a spokesman said Lord Blackwell would decide before April if and when to unwind his current responsibilities.