The society said the fall, from 960,000 to 540,000, meant the number of borrowers whose outstanding loans are greater than the value of their homes is now the lowest since late 1990. In the past six months, negative equity has more than halved.
Housing analysts and the Woolwich said that the drop was a sign of the continuing recovery in the market and an indication that further improve- ments were likely in coming months.
John Stewart, group chief executive at the Woolwich, said: "The halving of negative equity is excellent news for homeowners.
"Steadily improving confidence, underpinned by stronger disposable earnings growth, low interest rates and highly affordable housing, should ensure that the housing market recovery is sustainable."
He added that if house prices rose by 5 per cent in the next 12 months across Britain, as increasing numbers of experts predict, the vast majority of households would drop out of the negative-equity trap.
The Woolwich survey is based on a separate report by Halifax Building Society last week, which showed that house prices had risen by 3.8 per cent nationally in the past three months. Price increases have been even sharper in the south east of England.
The Woolwich said that the biggest falls in negative equity had been in the South-east and in London, with the number of households affected dropping by 80,000 and 75,000 respectively.
Nationally, however, the values of the homes of a further 1.25 million households exceed their mortgages by 10 per cent or less. That makes it difficult for them to fund a deposit on a new home out of the sale of their old one and meet the costs of selling and moving.
Martin Ellis, an economist at the Woolwich, said: "The results yesterday are not the end of the story for a lot of households."
He added that a combination of the increase in house prices and the fall in negative equity should improve the supply of homes for sale and increase transaction levels. "This means there is not so much pressure for house price inflation over the next six months, but, equally, prices should not start falling again."
Some economists believe that a too-rapid rise in house prices in the rest of the year could lead to higher interest rates.
Ian Shepherdson, UK economist at HSBC Markets, said: "I am not surprised at the Woolwich figures because this is something we have been predicting since last year.
"This also proves that it is not necessary, as many lenders argued last year, for negative equity to be resolved before a recovery in the housing market takes place. My guess is that negative equity should mostly disappear some time next year."Reuse content