(For Turnitin submissions, see the Turnitin guide. This method will not work for Turnitin.)
Go to the Assignments view of the Grade Centre.
Click the action link on the relevant column in the Grade Centre (the action link appears as a chevron icon when you hover on the title of a Grade Centre column).
Click Assignment File Download.
Select users as relevant or all users via the top check box. Note that it you want to select all users, you have to make sure all are listed on the page - you may need to click Show all first.
Then you’ll see a Download assignments now hyperlink. Click on this and open/save the zip file.