And full disclosure, I have not yet tried cycling in London.
But from a car drivers perspective, to me it seems that if by any chance, I made a contact with a cyclist even at breaking speed, I would injur the poor soul very badly.
And when I play that back but me being the cyclist... I can't get myself to get on a bike.
Having said that, I don't want to take away from your point that a lot of people will always feel too uncomfortable to ride in city traffic and I don't blame them. It's just that I often hear people complain about the safety of cycling in London and it's actually a pretty safe city to ride in (though it can definitely get better). The previous mayor was notorious for spending money on improving cycling in London and I think the stats bear that out. I left the UK in 2015, so I don't know what the current mayor is doing.
Not really disagreeing per se, but I think it's worth taking a look at the numbers. I got them from Wikipedia [1]. The lastest numbers they have are from 2017: 721 thousand journeys per day and 10 deaths per year. That's 0.0000038% chance of death per journey (although presumably about 40x that for serious injury, or 0.00015% per journey). While I appreciate that it's scary to ride in traffic, very unlikely to ever be killed on a bicycle in London. Not good as it should be, but over the last 10-20 years you can see that improvements have been made and I hope we'll see more to come in the future.
[1] - https://en.wikipedia.org/wiki/Cycling_in_London#Statistics