The death of a cyclist in London has reignited the debate about wearing helmets. There are arguments on both sides. I know of someone who spent six months in a coma after being flung across the bonnet of a car. Had she been wearing a helmet she would probably have walked away from the accident.
However experience elsewhere demonstrates that there are down sides. After Australia introduced compulsory helmet use for cyclist, the number of people cycling went down by 40% amongst adults and 60% amongst children
The Australian Transport Safety Bureau concludes that helmets do prevent and ameliorate injury. See: http://www.infrastructure.gov.au/roads/safety/publications/2000/pdf/Bic_Crash_5.pdf
However, the libertarian Institute of Public Affairs claims that ‘Even after 20 years and plenty of research, there is still no compelling evidence that Australia's compulsory helmet laws have reduced injury rates on a population-wide basis.’ http://www.ipa.org.au/publications/2019/australia%27s-helmet-law-disaster
This is a contentious issue and both sides feel very strongly. Look forward to an animated public debate.
Of course, there are alternatives: proper cycle routes, dangerous junctions made safer for cyclists, particularly in big cities with heavy traffic, and proper training – and testing – for drivers on how to behave around cyclists.