The Halifax survey is the latest to confirm the market slowdown
UK house prices saw an annual fall of 0.9% in April, says the UK's biggest mortgage lender.
The Halifax also said that prices dropped by 1.3% in April compared with the previous month, pushing the price of the average home down to £189,027.
The lender said it now expected a "mid-single-digit" percentage decline in prices in 2008.
But it expects bigger falls in Wales and the West Midlands, with Scotland bucking the trend with a modest rise.
Halifax's chief economist, Martin Ellis, said the decline in prices was driven by a squeeze on consumers' spending power and the rapid rise in house prices in the last few years.
"Completed property sales in March were down 20% on an annual basis," he said.
"The number of new buyers interested in home purchase fell for the sixteenth successive month in March, highlighting the decline in housing demand," he added.
According to the Halifax's figures, prices have fallen by 4.2% in the first four months of the year.
If that rate of decline continues for the rest of 2008 then the annual fall in prices will be nearly 13% by the end of the year.
The figures from the Halifax, the UK's biggest mortgage lender, are just the latest to show a big slowdown in the housing market, following rival mortgage lender Nationwide's report of a 1% fall in year-on-year house prices in April.
Earlier in the week the Bank of England said that new mortgage approvals had fallen to their lowest level since records began in 1990.
Mortgage deals have continued to rise in price, and their availability has fallen, despite recent falls in interest rates.
Lenders are demanding higher deposits as they tighten their lending criteria, partly because of a lack of funds due to the credit crunch, and partly because they fear further falls in house prices which would weaken the security of their loans to home buyers.
The Halifax said the number of mortgages approved to finance house purchases in the first quarter of 2008 was 41% lower than a year earlier.
It said this was the first year-on-year fall in house prices since February 1996, but the picture would not be the same across the UK.
It expects Scotland to see a "modest rise" in property prices in 2008, but areas such as Wales and the West Midlands to see bigger falls than the national average.
But Mr Ellis added that a balanced view of the state of the market should take into account recent history, with house prices nearly trebling - up 190% - in the ten years to August 2007.
"Price falls should be viewed in the context of the substantial price rises over recent years," he said.
"A growing economy, high employment levels, low interest rates and a shortage of new homes underpin housing valuations."
He expected the Bank of England to cut interest rates further in the coming months "as concrete evidence of an economic slowdown accumulates".
The Halifax's figures suggest that the number of first-time buyers entering the market has fallen sharply in recent years.
An estimated 300,000 first-time buyers entered the market in 2007, the lowest since 1980, the lender said. This compared with an estimated 900,000 at the peak in 1988.
The Royal Institution of Chartered Surveyors predicted prices would not fall too much further in the coming months.
"This downside is likely to be limited as the economy is still growing at acceptable levels, with employment figures remaining strong and mortgage rates actually coming down for many borrowers."
That was echoed by Peter Bolton King, chief executive of the National Association of Estate Agents.
"Rather than a dramatic fall that some doom and gloom merchants are predicting, it shows we are looking at a return to a more steady market rather than the fantastic price hikes we have seen in the previous 10 years," he said.
But Capital Economics warned that prices were likely to fall much further.
"With the economy yet to slow significantly and the labour market likely to weaken as the economy loses steam, this housing market correction is only in its early stages," said its property economist Seema Shah.