This latest rise pushed the three-month rate of growth to 2.7%, the highest rate since July 2011.
Annual growth now stands at 11.9%, with prices rising 42% since their post-Lehman low in March 2009.
Liam Bailey, Knight Frank’s head of residential research, said: "The strength of London’s luxury sector, against a backdrop of economic difficulties both domestically and globally, has surprised many over the past year.
"Ironically economic and even political turmoil have provided the impetus for growth – with a sharp growth in investors looking for a safe-haven location for at least part of their wealth portfolio.
"The sector leading price growth at the current time is the £1-£2.5million segment, which provides a perfect investment lot size for investors, prices in this price range have risen 14.4% over the past 12 months.
"Recent price growth reflects healthy growth in demand, new applicant volumes are up by 10% over the past year, compared to stock volumes which have risen by only 6%.
"The imbalance in supply and demand is most pronounced in the £5million+ sector, where applicant registrations are higher by 65% year-on-year.
"Over the past five years the ratio between the number of applicants registering to purchase properties in central London, and the stock of properties to buy has averaged 3.7. In the last three months, despite a weaker economic environment the ratio rose to hit 4.1.
"For the £5million market the ratio shifted from a historic position of 3.4 buyers per property to 6.4 – reflecting the historic undersupply at the upper end of the market.
"Our outlook remains that prices will rise 5% in 2012, driven in large part by international demand and relatively constrained supply.
"Finally, prices for prime property in the City and Fringe, an area we added to our index last year, kept pace with the wider PCL market in January, rising by an average of 0.8% across the month."
Charlie Hart, head of the Knight Frank City & East team, said: "We expect the earning power of the traditional local demographic to grow with the continuing success of the London tech and creative industries which have traditionally populated this Fringe area. The scarcity of product will drive demand and therefore pricing for the foreseeable future, enabling the City and City Fringe to sustain prime central London pricing levels."
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