Mortgage lending bounced back in March after being subdued in February.
Net lending, which strips out redemptions and repayments, rose by £5.42 billion during the month, according to the British Bankers' Association.
This was well up on both February's rise of £4.74 billion and the recent monthly average of £4.9 billion.
The jump in mortgage lending by the major banks was in line with figures reported by the Council of Mortgage Lenders last week.
The CML said lending soared to a new high of £28.31 billion during March, boosted by the housing market's traditional spring revival.
But it added that while lending usually started to pick up in the spring following a lull in house-buying activity during the winter months, the surge in lending during March was much stronger than could be accounted for simply by seasonal factors.
The Building Societies Association also reported a jump in mortgage lending during March, with net lending rising to £815 million, up from £629 million the previous month.
Commentators had taken February's subdued lending figures, combined with a drop in the number of new loans approved for house purchase, as a sign that the mini-revival in the housing market could be coming to an end.
But now they will now be waiting for figures from the Bank of England on mortgage approvals to gauge the strength of the market.
While mortgage lending rebounded during March, unsecured lending showed further signs of weakening.
Consumers reduced their credit card borrowing by £211 million, following a £160 million rise in plastic debt during February, the BBA said.
At the same time, lending through overdrafts and loans also fell by £145 million, after increasing by £456 million the previous month.
Both the BBA and the BSA also reported a jump in the amount consumers were saving, boosted by people putting money into ISAs in the run-up to the end of the tax year.
David Dooks, BBA director of statistics, said: "The contrast between stronger mortgage lending and net repayments of unsecured borrowing suggests that individuals are optimistic about the housing market, though careful about card borrowing, overdrafts or taking on personal loans. When deposit growth over recent months is also taken into account, the aggregate financial position of the personal sector as a whole does not appear to be under strain."
Howard Archer, at Global Insight, said: "The March mortgage lending and approvals data are clearly robust overall, pointing to a further firming in house prices in the near term at least."