However, Lloyds Banking Group advanced £1.3bn to businesses and households net of repayments during the period, amid an apparent improvement in UK conditions.
Banks and building societies in the official Funding for Lending Scheme (FLS) lent £1.6bn in the second quarter net of repayments. They were repaid £3.9bn net of advances in total in the preceding six months.
Details of the banks' activity are in the latest report on the FLS, which the Bank of England said showed it was having an effect in the UK.
"The FLS is continuing to support lending to the UK economy with a range of indicators suggesting that credit conditions are steadily improving for households and firms," said Paul Fisher, executive director for markets at the Bank of England. He added: "FLS participants collectively expect net lending volumes to pick up over the remainder of this year."
Howard Archer, a senior economist at IHS Global Insight, said the report added to the evidence that the FLS had led to a marked fall in the funding costs of banks, as intended. This has been passed on by banks in the form of lower interest rates.
Mr Archer said: "Mortgage approvals have picked up appreciably overall since the FLS was launched."
However, champions of small and medium-sized enterprises said the scheme appeared to have little impact on such firms, although SMEs were expected to be among the main beneficiaries. The scheme was launched by the Bank of England and the Treasury in June last year.
Phil Orford, chief executive of the Forum of Private Business, said: "Today's figures are disappointing with net lending to businesses and households down by £2.3bn (in total net of repayments) since June 2012"
Adam Marshall, Director of Policy at the British Chambers of Commerce, said: "The acid test for the FLS has always been whether it can improve the flow of credit to younger, fast growing companies that could end up being the wealth creators of tomorrow. Unfortunately the door often remains shut for many of these businesses who can find themselves being discouraged from applying for finance."
The second quarter figures for Royal Bank of Scotland and Clydesdale may spark renewed concern about conditions north of the border.
One in ten Scottish firms have had their overdraft cut in the past 12 months a survey for Close Brothers Asset Finance found.
The Federation of Small Businesses said it wants to see more competition in funding markets in Scotland. Royal Bank and Clydesdale dominate the Scottish market in areas like SME banking with Lloyds Banking Group, which owns Bank of Scotland.
The second quarter results reflect the continuing effects of big restructuring programmes at RBS and Clydesdale.
Royal Bank of Scotland, 81% owned by the UK Government,was repaid £2.8bn more than it advanced to customers in the quarter to June. Including net repayments of around £1.6bn in each of the two succeeding quarters, Royal Bank has been repaid £6.7bn net since the Funding for Lending Scheme began.
It has drawn down £750m of cut-price funding under the scheme.
With RBS still trying to clear up the legacy of costly over expansion in areas like commercial property lending in the previous decade, the figures may lend weight to calls for it to be split into a good and bad bank.
However, a spokesman said: "RBS is the biggest lender to UK businesses and has allocated £4.3bn of discounted loans to over 25,000 UK SMEs through the FLS."
He added: "Continued economic uncertainty means many businesses are still holding back from investing for the future, which is why we are proactively writing to our customers to advise them on how much more we can lend them."
Clydesdale, owned by National Australia Bank, was repaid £838m net of advances in the latest quarter. It has been repaid £1.6bn in total since the FLS was introduced.
A spokesman said the figures reflected the decision to transfer the subsidiary's commercial property loan book to National Australia and the results of a strategic decision to reduce activity in some other areas. He said Clydesdale was a keen participant in mortgage markets, adding: "We are actively looking for quality business banking opportunities."
He noted Clydesdale had funded its own activity and had not drawn any money down under the Funding for Lending scheme.
But Lloyds highlighted the fact it moved into a net lending position in the latest quarter, while continuing a long restructuring process.
The group lent £1.3bn net of repayments in the three months to June. It received net repayments totalling £983m and £3.1bn in the two preceding quarters.
A spokesperson said: "This growth comes despite the fact that the Bank of England figures also include our lending to certain 'non-core' sectors, which we are running down as we focus our efforts on sectors such as SMEs and First Time Buyers.
The group has received net repayments totalling £5.3bn since the FLS was introduced.
Barclays has lent £7.5bn net since the scheme was introduced, including £668m in the latest quarter.
Among challenger banks, Virgin Money has lent £2.4bn net, including £738m in the second quarter. Tesco Bank has lent £1.5bn, including £400m between April and June. Aldermore has lent £962m, including £252m in the three months to June.
Metro Bank has lent £281m, including £110m in the second quarter.