Hi Philip,
That log file link is only accessible to someone who can log in to your WP dashboard.
However, from your description, it’s most likely that the webserver has a timeout, and killed off the migration when it reached the uploads. You should go to the UpdraftPlus settings page, and restore *only* the uploads, and see if that works (since it’ll only be doing the uploads, it’ll have more time).
Failing that, download the uploads zip to your PC, unzip it, and upload the contents via FTP so that the resulting ‘uploads’ folder becomes wp-content/uploads. That’s all that is done with the restoration of the uploads backup – all the interesting stuff is done elsewhere (mostly with the database).
Best wishes,
David