It is the first such monthly increase since May.
The BBA figures, which take in Royal Bank of Scotland, Lloyds Banking Group, Barclays, HSBC, and Santander UK, show the stock of lending to non-financial companies by the major UK banking groups rose by a net £247 million in October to £295 billion.
This monthly rise, while modest in the context of respective falls of £1.46bn and £991m in August and September, was only the second increase this year. It was also in stark contrast to an average monthly fall of £1.29bn during the six months to September.
It was viewed by Howard Archer, chief UK economist at consultancy IHS Global Insight, as a possible sign the Bank of England and UK Government's Funding for Lending (FLS) scheme might be beginning to bear fruit.
This £80bn scheme offers funding to banks at below-market rates, with financial incentives to encourage them to lend.
Mr Archer said: "While lending to non-financial companies in October is still extremely low and not too much should be read into one month's data, the small rise could be a first tentative sign the Funding for Lending scheme is starting to have some positive impact in supporting bank lending to companies."
Some firms continue to report trouble in securing loans at all, or in lining up borrowings with acceptable rates of interest and arrangement fees.
Banks cite a lack of demand for borrowing from businesses in explaining weak net lending figures.
Mr Archer said: "It needs to be borne in mind that low lending levels to companies have reflected demand as well as supply factors.
"There is low demand for credit, with many companies wary about borrowing and investing in the current difficult economic environment ... Many companies are looking to pay down debt."
He cited the large and increasing number of banks signing up to the FLS and the fact bank funding costs had fallen.
He added: "How much companies want to borrow remains questionable.
"But it is important for UK growth hopes that all companies who are in decent shape and who do want to borrow – whether it be to support their operations, lift investment, explore new markets – can do so, and at a non-punishing interest rate. This applies to all companies, whatever their size."