Competition among mortgage lenders has intensified, brokers say, with a greater willingness to lend to those without huge savings.
Brokers say that, in recent years, the best deals were only available to those offering a large deposit, but there were now signs of change.
However, a new record rate five-year mortgage, newly on sale, still requires a 40% deposit.
The HSBC mortgage, with a rate of 1.99%, also comes with a £1,499 fee.
Earlier this month, lenders told the Bank of England that demand for new mortgages had fallen for a third successive quarter.
The bank's Credit Conditions Survey found that demand for mortgages for high-value property saw the biggest fall since the third quarter of 2008.
Having been concentrated on this market, there are now signals that banks and building societies are casting their net a little wider.
The survey found that lenders were showing a greater willingness to lend to borrowers who were only able to offer a deposit of less than 10% of the property's value so far this year.
"The lenders are stepping up the fight to attract new borrowers and rates are still getting cheaper," said Aaron Strutt, of broker Trinity Financial.
"First-time buyers with a 5% deposit can take a fixed rate just over 4% and if they can raise a 10% deposit the rates are as low as 2.69%.
"A few years ago borrowers needed a 40% deposit to access a really good mortgage, but now rates are cheap for most new buyers.
"HSBC's latest fixed rate really takes the mortgage price war into new territory and even cheaper deals may well filter through to the market."
Nearly two-thirds of mortgage holders are sticking to a variable rate as the Bank of England's base rate is showing no signs of rising from its historic low of 0.5%.
Charlotte Nelson, of financial information service Moneyfacts, said that 15 lenders had cut mortgage rates in a week - partly to try to tempt some variable rate customers back to fixed rates.
"The competition to be the lowest in the mortgage market shows no signs of stopping and is great news for borrowers," she said.
All this appears to be good news for first-time buyers struggling to afford a property.
Yet, there are still significant hurdles for these, generally young, potential property owners.
The most eye-catching deals - such as HSBC's home loan which is said to be the first five-year mortgage with a rate of under 2% - can still come with significant fees and deposit requirements.
Ms Nelson said borrowers needed to consider the whole package to work out the cost of the loan.
Borrowers also face strict affordability checks that test whether they are able to cope with an interest rate rise.
Property website Rightmove also reported a rise in average asking prices, suggesting homes are becoming less affordable for first-time buyers.
It said new sellers' asking prices increased by 1.6%, or £4,381, in April compared with March to reach £286,133 on average across England and Wales, surpassing a previous peak reached last June.