Mortgage borrowing by house buyers is recovering, the Council of Mortgage Lenders (CML) has said.
The number of loans made to home buyers rose by 25% between February and March, to 45,000.
And borrowing by first-time buyers rebounded faster than that by existing home owners, the CML said.
But it warned that mortgage rationing might continue for many years unless the new government helped lenders raise finance.
"Today's figures indicate there is currently some momentum to house purchase lending," said the CML's director general Michael Coogan.
"But for the sake of the future health of the housing and mortgage markets, the new government will need to focus on the critical issue of funding and how to address the issues arising from the repayment of the emergency support provided during the financial crisis," he added.
"The UK is at risk of a chronic under-supply of credit - and the rationing of mortgages for customers - for years to come."
Lending to all house buyers in the first quarter of the year was still 35% less than in the last three months of last year.
But the CML said that not too much should be read into that comparison.
"No trend can be inferred from this... given the distortion caused by the end of the stamp duty holiday in December," said Mr Coogan.
The CML argued that year on year, lending to house buyers had now risen for the ninth month in a row.
And it pointed to an improvement in the position of first-time buyers.
For the second month in a row, the average deposit they had to put down stood at 24% of the purchase price, slightly less than the average 25% they have had to put down since the start of 2009.
Between February and March, the number of loans made to first-timers rose by 27%, compared with a 24% increase for existing home owners.
"Only time will tell if this genuinely reflects a tentative sign of easing, but for the time being deposit constraints remain tight in all areas of lending," the CML said.
With house prices rising over the past year, lenders have become slightly less wary about lending.
Earlier this month, the financial information service Moneyfacts reported that the number of mortgage deals available was 36% higher at the start of May than it had been at the start of the year.
Although there were still very few deals with 0% or 5% deposits, the number asking for a 10% or 15% down-payment had gone up from 461 to 520.
Despite this, lenders have been warning that they face a huge problem in the next few years.
Banks and some larger building societies have to work out how to repay more than £300bn in emergency funding given to them by the government during the banking crisis in 2008.
The need to repay that money is likely to mean continued rationing of funds for mortgage borrowers.
So far, no plans have been forthcoming, either from within the banking industry or from the UK's financial authorities, to deal with the matter.