Property prices in London may steady but will generally not fall. However, there is a often a big gap between asking prices and sale prices. Asking prices may certainly become more realistic. Also, there will be falls in certain locations and market segments. There is a huge amount of "luxury" flats coming on the market in centralish London over the next three or four years. I've seen how a glut of new build flats at Canary Wharf/Greenwich has dampened prices there and am sure that it will happen elsewhere.
One point that I note, however, is that people who talk about the jumps in London property prices are not comparing like-with-like. The house that sold last year for four times what it sold for in 1999 may have had a loft conversion and rear extension, increasing its habitable space by 20%, it may have been rewired, redecorated, had a new kitchen, bathrooms, etc. Even without any extension/loft conversion, there is a big gap (as much as 20%) in price between a house that has been fully refurbed in the past five years and one that hasn't been refurbed in 25 years. (Although some refurbs can be less than ideal - I viewed one house where each room was painted a different neon colour.)
I do get pretty sick of listening to people whinging on this thread about how they can't afford to buy somewhere in London. The problem with a lot of local people is that the 1950s - 1970s gave them the mentality that they would be "given" a property by the council at some ridiculously sub-market level rent (subsidised by everyone else). My wife and I own a six bedroom Victorian terraced house in zone 3. We came to London, separately, ten years ago and lived in house shares in ex-council flats where the living room was another bedroom until we saved deposits to buy small flats of our own in less desirable areas of zone 3/zone 4 which we paid off as quickly as we could. We sold our flats and pooled our money to buy this house. We didn't drink, we didn't smoke, we didn't have satellite TV, we didn't go to any festivals, we made our own packed lunches and took them to work, we worked second jobs at weekends. After we met and got married we didn't have children until we had bought our house and got the mortgage on it (because if we had, then we shouldn't have been able to get the mortgage).
A lot of the problem is the mentality of some of the "locals", like gypsygirl on this thread sneering about Lewisham. House prices are about supply and demand. She might consider Lewisham overcrowded and dirty but more people want to live there and not in whatever corner of Kent she has moved to. In particular, immigrants have high aspirations and are worried about the racism and culture of low aspirations they encounter when they go towards the edges of London - teenage girls whose aspiration in life is to become a hairdresser or go to beauty "college". The whole grooming scandal is an illustration of the culture of teenage sexual promiscuity that pervades working class "culture" in this country.