All of the instructions available online for deleting a disk from a non-existent VM relate to the older Azure UI which does not contain the same menu commands as the new Portal. Therefore I need instructions for deleting an orphaned disk using the new Azure Management Portal. Instructions for the old portal are worthless for this action.
Azure VM disks are stored in Azure Storage (blob containers).
Open http://portal.azure.com, click All Resources and locate the storage account, which you can manage there (for the entire account).
Or, to remove just that blob, get the Storage Explorer from here: http://storageexplorer.com/ - enter your credentials and use it to remove the required blob.