There are various insurance policies to cover various risks.
If you have a mortgage to pay and work, there are policies that provide some relief to cover the mortgage costs if you cannot work.
If you are injured, the NHS funds your emergency treatment - or you may invest in Health Insurance for a broader scope of cover on medical costs.
What cost incurred by you would you want the insurance to cover the risk on? - it isn't often people want a sum of money just for the sheer inconvenience factor of, say, breaking an arm.