The estate agents said the gap between offers and asking prices had closed to just 2.2% in January.
The average property sold for 97.8% of its asking price, the smallest gap between asking and sale prices since June 2011.
This compares to an average of 95.3% in January 2011.
While the gap between asking and sales prices has fallen by 2.5% during the last year in the capital, the improvement has been much smallest nationally.
Across the country as a whole, the average sales price achieved was 92.5% in January, compared to 91.9% in January 2011.
Heightened competition for property in the capital has been the key factor. In January, an average of 17.9 buyers registered for each property placed on the market, the fiercest competition on Marsh & Parsons’ records.
The competition among buyers is higher than the previous peak of 16.7 applicants per property in September 2011 and represents a significant increase from 14.2 a year ago.
Peter Rollings, chief executive officer of Marsh & Parsons, said: “While prospective buyers may often be able to secure sizeable discounts in other parts of the country, the same cannot be said of prime London.
“Swelling demand for a limited pool of homes on the market has turned central London into a real seller’s market, and well priced properties are encouraging multiple bids.
“Fierce competition means that buyers can no longer simply test the waters with an unrealistically low bid, or they face losing out to determined rival bidders.”
Rollings added that rising property prices in the capital had been driven by the underlying contrast between the appeal of prime London to buyers and the lack of properties available.
“Investors are holding onto properties for the long-term, rather than looking to cash-in on short-term capital gains,” says Rollings.
“In turn this is further limiting supply in prime parts of London. With space for new building limited - and central London set to remain as one of the most sought after cities to live in the world, home sellers will continue to have the upper hand in the sales process.”