The increase in total lending recorded by the Bank of England was the biggest since records began in March 2011. It may be seen by some as a sign that efforts to encourage banks to lend are paying off.
However, the fact that net lending to SMEs fell for a third month running may fuel fears minnows are having a hard time compared with bigger fish.
The Federation of Small Businesses in Scotland said conditions had started to improve but a majority of its members still believe credit availability is poor.
A spokesman said: "Our research suggests that an increasing proportion of businesses that apply for bank finance are successful, though two in five applicants continue to be rejected."
He added: "Around half of our members still believe that bank finance is unaffordable."
The Bank of England figures could prompt renewed debate about whether falls in lending reflect lack of demand for credit or if firms are not applying for funding because of the costs involved and concern about how lenders will react.
The FSB said more work needed to be done to better connect the small business community and the high street banks.
Last week research by the Institute of Chartered Accountants of Scotland found "debt-shy" SMEs were reluctant to borrow funds for growth because of a lack of trust in banks and a resistance to yield control of the business to outsiders.
Howard Archer, UK economist at IHS Economics, noted reports by the Bank of England's regional agents in May showed demand for credit had increased overall but remained sluggish "especially among small and medium-sized enterprises, as trust in banking relationships remained weak".
The BBA, which represents banks, said the Bank of England data showed gross lending to SMEs, ignoring repayments, has risen every month since April 2013 on a year-on-year basis.
Gross lending to SMEs, excluding overdrafts, was £4.3bn in May, up from £3.4bn in the same month in 2013. It reached £4.1bn in April.
The BBA believes the net falls in lending may reflect the desire of SMEs to use the cash they are generating to repay debt.
It noted 82 per cent of SMEs interviewed in the latest bank-funded SME Finance Monitor said they did not seek external finance, nor did anything stop them from doing so.
The number of mortgage approvals made to home buyers dropped for a fourth month running in May, to the lowest level since June 2013.
Some 61,707 mortgages worth £10 billion were approved, 19 per cent below January's peak of nearly 76,000. The launch of stricter lending rules may be impacting on the market. Net lending to non-financial firms fell by £2.4bn in April and £2.3bn in March.
Net lending to SMEs fell by £629m in April and £1.1bn in March.