Slightly more than half (52.9%) of all local authorities across the UK experienced an increase in housing prices over the month to June.
In London, house prices rose by 0.4% over the month to June, adding £1088 to the value of a typical house in the capital.
While the annual decline in London is now at its shallowest since January 2009, prices are still down by 15.3% compared to June 2008.
Kensington and Chelsea remains the most expensive borough in the country, but with an annual house price of £628,159 it has experienced the largest annual decline of 27.3% (a loss of £236,226 in monetary terms).
Robert Bartlett, Chesterton Humberts CEO, said: "We’ve reached a confusing stage in the property market cycle where prices in most of London appear to have stabilised – and are rising in prime central London – while outside of London prices continue to fall marginally, although several areas have started to bottom.
"Stock shortages are becoming severe in parts of London and the South East which is helping to buoy prices. Owners who would normally be considering up or downsizing are putting off the move due to low mortgage rates and the aggravation of having to arrange a HIP before testing the market.
"Reports of an upward trend in property prices are perplexing for home owners in areas still affected by price falls, who can’t understand why they are not seeing viewings and offers for their house.
"Experienced agents with the benefit of a national network like Chesterton Humberts are able to see the bigger picture and guide owners appropriately."
Douglas McWilliams, Chief Executive of CEBR, said: "House prices appear to be stabilising after 13 consecutive months of falling prices. It is always difficult to interpret data from the housing market in summer, because people tend to buy houses at around this time of year when the weather is warmer and the days are longer.
"We may yet experience further small falls in prices but the worst of the house price contraction is almost certainly behind us."
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