The Clydesdale Bank, and its sister Yorkshire Bank, have faced a rise in bad debts, according to a market update.
The banks' owner, National Australia Bank, said it remained "cautious" about the state of the UK economy, following the new government's budget in June.
It said British market conditions remained difficult, and demand for credit remained subdued.
However, it said business confidence was showing some signs of improvement.
Clydesdale and Yorkshire claimed they remained on track to deliver £10bn of gross new lending to businesses and mortgage customers by October next year.
The charge for bad and doubtful debts rose in the second quarter of this year, though they were better than in 2009.
Those loans that are 90 or more days overdue, added to gross impaired assets, increased to 3.36% of gross lending, from 2.98% in the first quarter.
"Trading conditions remain challenging for businesses, and this is reflected in asset quality measures," according to the trading update.
Lynne Peacock, chief executive of National Australia Bank's UK operations, said: "We continue to follow a very steady and prudent course. While the signs of economic recovery remain encouraging, our strategic direction is unchanged.
"Firmly focused on growing our existing business, we remain committed to supporting our existing customers and are on track to deliver £10bn of gross new lending by October next year."
The parent company, which is one of Australia's big four banks, claimed its figures were "solid and sustainable" for the second quarter of 2010, though they fell below analysts' expectations and the NAB share price fell.