I finally tracked down the source of these numbers to the DfT report, specifically Table RAS50005 on page 73. Some conclusions drawn by the Guardian author and various commenters are bogus based on the published data:
The table relates to all road accidents, not specifically to fatalities, so "cycle deaths" is bogus
The numbers are quoted from the column on factors attributed to a pedal cycle, there's no way of knowing from these percentages what percentage are ascribed to a car, so the "biggest single contributory factor" is bogus
Multiple contributory factors may be ascribed in an accident, so the implication that a total of 51% implies a majority of accidents 'caused' by a cyclist is bogus... there might well be a higher total for cars; I don't think this information is deducible from the table because it doesn't separate car-bike from car-car or car-motorbike.
There are more detailed studies available, e.g. the Transport Research Lab report from 2009, which show that the majority of adult cyclist fatalities arise from causes ascribed to motorists.
A poster called robjordan posted: