These threads always strike me as odd, because those telling people what to do seem to do so on the basis of no evidence at all.
Assumptions I see here:
That cycling in London is particularly dangerous - most experienced cyclists would say not, but you need stats.
That wearing a helmet will make what is assumed to be dangerous as per the above into something safe enough for mass participation. Rather odd again, the assumed hazard is large heavy vehicles and it is odd to believe that plastic hats can somehow neutralize this threat.
That helmets significantly enhance cycle safety. This belief is usually based on assertion and bluster 'well it must do'. Contrary studies are dismissed as nonsensical, and in the rare event that the poster has any study in support, these are to be treated as unimpeachable.
That pseudomedical anecdotes are of great value - e.g. my hairdresser's brother fell off his bike wearing a helmet and hit his head and didn't die, therefore the helmet saved his life, regardless of factors such as whether he would have hit his head in the first place without a helmet, or the physical limits on a helmet's effectiveness.
That cycling is somehow inherently dangerous, compared with say walking or other everyday activities not deemed to require special equipment, and therefore safety gear is necessary. (Hint: walking is more dangerous.)
That you can make analogy with other safety apparatus that operate in different ways and therefore prove your point - e.g. You wouldn't drive without a seatbelt, therefore a helmet is required for cycling. Of course more logically, if cycling requires a helmet, so should cars. Or motorbikes require helmets (which are much better than cycle helmets, being bigger and heavier), therefore so should bicycles (why not leathers also???).
And so on, almost never with any logical reasoning.