The survey found that access to a mortgage was viewed as a barrier to buying by just 49% of people, compared with 55% back in June and 58% in March.
The survey also found that over half (58%) of respondents believe that now is a good time to buy, and that respondents expect property prices to rise by 1.6% over the next year.
However, a lack of job security remains the most significant barrier to property purchase, chosen by 58% of respondents. With unemployment forecast to rise into 2010, this is likely to remain a critical influence on the confidence of house buyers.
Commenting on the survey's findings, Paul Broadhead, head of mortgage policy at the BSA, said: "It is clear that home buyers are increasingly viewing the property market in a positive light as confidence increases in the market.
"The majority of respondents believe now is a good time to buy. With mortgage availability perceived to be increasing, prospective buyers are more confident of securing funding to purchase a property.
"However, buyers are clearly treading with care, and worries over job security continue to deter many from buying. Lack of job security remains the most significant barrier. With unemployment forecast to rise into 2010, this is likely to remain a critical, negative influence on the confidence of house buyers, and deter them from returning to the market.
"Raising a deposit is also seen as a barrier by over half of the respondents to the survey, and this may further constrain house price growth in the future."
