In the UK, the averages suggest that you are slightly less likely to be killed cycling two miles to the shops than you are making the same trip on foot, but slightly more likely to be seriously injured.
Over the decade from 2001 to 2010, there were 28 cyclist fatalities per billion kilometres cycled compared to 35 pedestrian fatalities per billion kilometres walked. For serious injuries, it goes the other way: about 400 people killed or seriously injured per billion kilometres walked against 550 per billion kilometres cycled. (Full Fact summarises Department for Transport "Passenger casualty rates for different modes of travel".)
Other sources give slightly different numbers, and obviously these are all population averages and individual situations vary. Pedestrians include many relatively vulnerable people — children and the less abled and elderly — who are rarely found cycling, at least in the UK, so able adults are relatively safer walking than those figures suggest. On the other hand, somewhere like Oxford is, while better for pedestrians than most UK cities, vastly better for cyclists, so anyone in Oxford is relatively safer cycling.
In any event, the risks involved in walking or cycling this kind of trip are at least roughly the same. The difference between them is much smaller than the difference between either one and catching the bus (clearly safer) or the difference between driving a car and riding a motorcycle. So why is it that people who wouldn't even contemplate wearing special high-visability clothing or a helmet for a walk to the shops not only do so when cycling the same route, but try to insist on other people doing so too?
Answer to rhetorical question: This is driven by a media and policy obsession about helmets which is largely a convenient way of blaming the victim, so the first question when an accident involves someone on a bicycle can be "were they wearing a helmet and flashing brightly" and not "was the vehicle driver grossly negligent" or "should someone be prosecuted for putting an 80cm cycle lane right next to 50mph traffic".
Looking at this study along with the DFT data suggests that, roughly, for every fatality cycling there will be ten serious accidents, a hundred less serious hospital presentations, and a thousand minor accidents.
However any measure of risk obviously needs to be weighted - all the non-serious and minor injuries put together are probably about the same concern as the fatalities and serious injuries, even if the latter are 100 times less frequent. Different people will weigh things differently here, but I can't see this changing the overall risk comparison that much. And I've never heard advocates of helmet-wearing laws argue that they will prevent hundreds of thousands of scrapes and abrasions.
The biggest problem with the studies of helmet wearing I've seen is that they lump together all kinds of activities involving bicycles: sports cycling and mountain-biking and long-distance commuting with everyday utility cycling and boring slow commutes. The meta-analyses also, invariably, exclude data from the Netherlands... (Apparently people wearing helmets there are vastly more likely to be admitted to hospital, because no one wears helmets unless they are racing or mountain-biking. They still manage one third the KSIs per kilometre of UK cyclists, despite having much higher numbers of relatively frail people cycling.)