Earlier quoted context omitted.
London has over 6,000 cycles that are registered with clearly visible numbers, and with the cyclist on the bike known. It's called the cycle hire scheme. In this time, not a single cyclist has been tried for anything, and yet several of them have been killed by HGVs. Registrations aren't stopping cyclist fatalities.
It is notable, though, that almost all London bike deaths seem to be from being run over by HGVs. Cyclists (stereotypically) loathe cars, but are not killed by cars. I don't really have own experience of London traffic, but from reading newspapers, it looks like you should do less to cars and more to heavy goods vehicles and buses.
It really is just the HGV, and the construction industry related HGV at that.
"You should"... well I and very many others are. However the essence of the issue appears to come down to a mix of the economics of being a HGV driver, local politics, and the nature of congestion and traffic in an old city.
The economics is that HGV drivers are paid by the job. They are effectively incentivised to complete a job as fast as possible to increase their earnings. Being paid to go faster isn't very compatible with driving safer.
The politics is a blend of TfL (Transport for London) not having the authority to re-design many junctions, local councils wishing to maximise traffic flow, and residents not wishing to tolerate construction traffic outside of work hours. This means that construction traffic can only operate during the work day (when it's most congested), on roads that were not designed for such a volume of HGV traffic, with junctions not designed for cyclist safety or space. A very recent HGV fatality is directly contributable to Westminster Council refusing to implement recommendations by TfL to make a junction next to a bridge safer... this was last week, you'll find the info online easily enough.
The last point relates to the city itself. You'll see from other comments that the best thing to do is to segregate cyclists from the motorised traffic, but that requires space. London is an old city and we cannot move buildings and streets to accommodate this segregation outside of more than a handful of wide boulevards and roads (such as the Embankment where it is being done). We can only achieve segregation by turning 2-way streets into 1-way streets (as is being done on Tottenham Court Road), but even then that adds pressure to surrounding roads. There are limits to what can be done to provide extra space and re-designs to existing junctions and roads.
Possibly the best thing is the cross-London move to a 20mph speed limit.
But the biggest remaining thing that could be done might be to change the economics of the construction industry in London. Perhaps just place an outright ban on HGVs that do not meet some strict requirement for operating in such a busy metropolis. Perhaps just change the status of road fatalities by HGVs such that they are considered a Health and Safety issue of the work-site that the work is being done for... i.e. if the victim's family can sue the construction site for death then perhaps that will change the job incentives enough to bring in safety features, etc.
But yeah, we are on it.