Attention has been drawn elsewhere on the forum to the publication of the latest accident stats. Table 23c has the data for single vehicle accidents. For pedal cyclists, this has two columns, one where a pedestrian was involved, one where they were not ie cyclist came off or hit something other than a vehicle.
A total of 458 injury accidents were recorded for the year. There were 464 casualties of all types so I can only assume there were six tandems involved where both riders were injured. Of the casualties 6 were fatal, serious 177, leaving presumably 275 minor injuries. Obviously, in many cases where a cyclist comes off, even if they are injured they will never come to official attention. Even so, it seems unlikely that there were fewer than 500 injury accidents of the 'no other vehicle involved' type throughout the country over a whole year.
Reference is made in the stats and elswehere to the significant difference between police reports and hospital admissions. Here's one part of the reason.
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Edit: The instructions in IRC's link date from 2005, way after my time so I'm out of date.
Scrolling down from the bit he quoted there is this:
which in the document is in a large bold-faced font to emphasise it.The STATS19 requirement is clear that all accidents involving non-motor vehicles such as pedal cycles and ridden horses on 'public roads' (see 2.4) should be reported, regardless of motor vehicle or pedestrian involvement.
From the data I've quoted, it's not changed much.