Some surveys have suggested a low supply of homes for sale
The number of loans handed out for house purchases in the UK rose by 16% in April compared with the previous month, according to lenders.
But the figure remains 28% down on the same month the previous year, the Council of Mortgage Lenders (CML) said.
The data adds further evidence to indications of a spring bounce in the housing market.
However, first-time buyers still have to put down an average deposit of 25% of the value of their new home.
In April, the average amount borrowed by first-time buyers for a home loan rose slightly to £96,000 - the first rise since May 2008.
The data is the final set of figures relating to the state of the mortgage market in April, and effectively echoes lending data from earlier surveys.
The figures confirmed a rebound in the popularity of fixed-rate mortgages, with homeowners predicting that interest rates are unlikely to fall further.
In January, 48% of new home loans were fixed-rate deals but this proportion rose to 69% in April. The average rate charged on those deals in April - of 4.83% - was the lowest paid since January 2004.
"With the interest rate cycle now at its floor, an increasing proportion of borrowers are taking out fixed rates, including for longer term periods of five to 10 years," said CML head of research Bob Pannell.
"With expectations for rates to remain low in the near future, shorter term fixed-rate deals are less appealing than attractively priced variable-rate deals."
However, Nationwide Building Society is reported to be increasing the cost of its fixed-rate deals on Friday, by up to 0.86 percentage points.
A 0.86 percentage point rate increase on a £150,000 interest-only mortgage will increase the total cost over five years by £6,450.
'Less to lend'
Part of the reason for some analysts suggesting that other lenders were likely to follow suit was the sharp increase in swap rates - the amount banks charge each other for borrowing and lending money over a fixed period of time.
The number of people remortgaging has dropped again
"Lenders are now hiking their fixed rates, partly because swap rates have increased dramatically over the past few days, partly because lenders have too many applicants and too little to lend, and partly because they can," said Andrew Montlake, director of mortgage broker Coreco.
"What concerns me is that many people coming to the end of their existing mortgage products are still reverting to, or being forced to revert to the standard variable rate (SVR), which could come back to bite them should rates rise sharply."
Rising interest rates would have a positive impact for savers, however, who would see returns they receive from their savings accounts go up.
Few houses for sale
The number of loans for house purchases stood at 35,500 in April, the CML said.
"There are tentative signs of house purchase lending stabilising, but we need to see considerably higher transaction levels to underpin house prices," said Mr Pannell.
Recent house price surveys have suggested some pent-up demand, but pointed out that a squeeze in the number of homes on the market has pushed up the prices of those that were available.
The number of people remortgaging dropped to 31,000 - down 22% compared with the previous months and a fall of 65% compared with a year earlier.
This was the result of strict lending criteria for the best deals, the lenders' group said.