I feel your pain, although we are looking to rent, not buy.
I think London has too many unique factors to make any substantive predictions (in model-speak, it's a serious outlier). The normal rules of supply and demand don't really apply.
You could compare it to a city like New York, which is also very unique. As far as I know, in New York, once prices go up in an area, they do not come down.
Or another unique and expensive city, Washington DC. You did have a big decline in housing prices there at one point, but that was because of race riots, insane levels of drug violence, a crackhead mayor... once things calmed down, prices shot up again.
It's always possible that prices will come down in London, but that will likely require a lot of very impactful things to happen. So if you really need to move, I think you may have to adjust your wishes rather than wait on the market.
I know it really, really sucks though. I think it's a crime that housing costs so much, it's a basic life necessity.