House prices rose by 1.2 per cent during April and May, according to Nationwide Building Society. It said that the increase was because of huge demand from buyers and a shortage of properties to choose from.

Estate agents have reported that good-quality homes are in such short supply that gazumping — when a buyer makes a higher offer than one already accepted by the seller — is making a comeback in some areas.

The average price rose from £151,861 to £154,016, the society’s latest monthly housing market survey showed. They have fallen by 11.3 per cent in the past 12 months, a “significant improvement” on the 15 per cent annual decline recorded in the 12 months to April. Prices are down by 0.5 per cent since March, the smallest fall over three months since January last year.

Martin Gahbauer, chief economist at Nationwide, said: “The improvement is consistent with signs of stabilisation in several other economic indicators and suggests that any further price declines may occur at a less rapid pace than in 2008.”

The figures support mounting evidence that conditions in the housing market are past their worst point, a view increasingly shared by economists and estate agents. However, Nationwide said that the impact of rising unemployment and tight access to credit would continue to depress prices in the near future.

Forecasters expect prices to fall by 5 to 15 per cent before hitting rock-bottom, although discounts negotiated on some properties have already exceeded total peak-to-trough decline predictions of 25 to 30 per cent. Transaction levels have shown signs of recovery over recent weeks, from a low of five a month per estate agent to ten last month, according to the National Association of Estate Agents.

A large proportion of buyers who have taken advantage of lower property prices have been cash-rich investors buying distressed and repossessed stock, or homeowners with a lot of equity wishing to trade up and take advantage of lower mortgage rates. Buyers without big deposits have been thwarted, although lenders are introducing more generous deals. Lloyds Banking Group launched a first-time buyer mortgage last week for those with deposits of 5 per cent.

Nationwide, which bases its figures on prices paid by its mortgage customers, attributed this month’s rise to an improvement in the sales-to-unsold stock ratio, a measure that has stabilised as fewer new properties have come on to the market. A preference for letting rather than selling among homeowners who need to raise cash, and the slowdown in construction of new homes, are regarded as the causes of the chronic lack of supply.

Simon Rubinsohn, chief economist at the Royal Institution of Chartered Surveyors, said: “The new instructions series has fallen consistently for the past two years as would-be vendors have either turned to the rental market or decided to stay put, rather than attempt to move. This has left little fresh stock.”

Nationwide said that difficulty finding tenants and the likelihood that some owners would no longer be able to afford to stay put as unemployment continues to rise means that more second-hand properties will come on to the market in the coming months.

The supply of new homes is likely to worsen, as housebuilders have struggled to raise cash for new developments and existing schemes have been mothballed due to a lack of funding.