I think that, as well as the green form, an additional step should be added to the process of requesting a cremation, collecting ashes and arranging a funeral. This should be to prove that the person arranging the funeral or collecting the ashes is the next of kin or executor of the will.
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I don't think that the green form and death certificate should be sufficient proof to confirm someone has the right to collect ashes or organise a funeral. This will prevent families being caused distress by not being able to rightfully collect and bury ashes of a loved one.