These "rules of the thumb" have been accurate for decades, lately the numbers "went crazy", partially because of the increase of costs for new houses, partially because of the lowering (or stagnating) of income, partially because of increases in taxation (either on personal income or house related taxation).
The phenomenon is not restricted to the UK, or to the London metropolitan area, here is a data point about Italy (the article is in Italian but the leading graphic is clear enough):
https://www.idealista.it/news/immobiliare/residenziale/2017/...
which is not that bad in Google translate.
The three bars are respectively employees (dipendenti), independent professionals (autonomi) and retired people (pensionati) which represent roughly three different levels of income, average, high and low.
Another approach is to take your salary, max out your pre-tax retirement contributions, find out what dollar amount you need to maintain your current lifestyle in non-accommodation costs, set aside at least a few hundred $ monthly buffer, then whatever's left will be your budget for housing.
So even if you can save up, you still can't buy a house.