House prices dipped by 0.2% in January, as analysts predicted that the market could tilt further in buyers' favour over the coming months.
The average house price is £162,228 following the second monthly drop in a row after a 0.2% fall was also recorded in December, Nationwide's latest house price index said.
But the lack of new homes coming to market means prices are likely to drop only modestly or move sideways in the near future, the building society said.
Buyers are being offered some of the cheapest ever mortgage deals, with initial mortgage payments running at their most affordable level since 2003.
But Nationwide said the weakness in demand from buyers was partly due to the hurdle many face in finding a deposit.
Household budgets have been under intense pressure due to high living costs and deteriorating employment conditions.
Borrowers are also expected to have a tougher time raising a mortgage this year as lenders tighten their criteria amid the weak economic backdrop.
Robert Gardner, Nationwide's chief economist, said: "Given the challenging conditions prevailing in late 2011, with the UK economy contracting in the final three months of the year, it's not surprising that house price growth softened at the start of 2012."
He continued: "The demand/supply balance may move further in favour of buyers in the months ahead. The economy is not expected to gather much momentum until the second half of 2012 at the earliest, which suggests that labour market conditions and buyer sentiment may be slow to improve.
"Nevertheless, with the flow of properties coming on to the market still more of a trickle than a flood, house prices are likely to continue to move sideways or only modestly lower in the months ahead."