The Bank of England has reported that net mortgage borrowing by households was little changed at £3.8 billion in September.
The stability in the monthly flows has left the annual growth rate unchanged at 3.2%.
Growth rates have now remained close to this figure for the past three years.
Mortgage approvals for house purchase (an indicator for future lending) were also broadly unchanged in September, at 66,000, and remained within the narrow range seen over the past three years.
Mortgage approvals for remortgage strengthened slightly to 49,000.
Andrew Montlake, managing director of mortgage broker Coreco, said: “Amid the mayhem, mortgage approvals are holding up exceptionally well.
“Mortgage approvals could rise further given the new affordability guidelines for mortgage prisoners published by the Financial Conduct Authority this week.
“Remortgages, as ever, are surging as people batten down the hatches to ride out the potential storm ahead.
“Likewise, a lot of people are worried that house prices could rise sharply if a deal is reached and we leave the EU on agreeable terms.
“Many homeowners have been living under a cloud of uncertainty since the global financial crisis and are now well accustomed to chaos.
“Rather than going to ground, people are proving philosophical and are getting on with their lives.”