You can use Chrome to copy folders and files from D: drive to your OneDrive for Business storage.
In order to do this you will need to login to the OneDrive web page with your SHU Office 365 account, which is usercode@hallam.shu.ac.uk and then you can either drag and drop files and folders from D: to the Chrome Browser window or use the Upload menu options within the browser window.
See Upload and save files and folders to OneDrive for Business

The limitation with this method is that empty files will not be copied, though again, this shouldn’t affect many people.

See the video showing how to use Chrome to copy files from D: to OneDrive for Business.