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You are not alone. Transport for London found safety concerns as the biggest reason people do not cycle in London. Interestingly, many people who do cycle also considered it too dangerous.

For what it's worth, your risk from diseases of inactivity (diabetes, heart disease, etc) are far greater than the risk of cycling, even with poor infrastructure. Most people who take up cycling to work see an increase in life expectancy.

The solution is to separate cyclists from motor traffic on all major roads and introduce 30kmph limits on quiet roads. The Netherlands did this and has far lower accident rates, despite having more children and elderly people cycling. They don't wear helmets either!