If your "new space" is the result of a new install on a larger hard disk, and you haven't synchronized with U1 on that install yet, then simply logging into U1 there should result in everything under the ~/Ubuntu One folder being downloaded again, and if they were in a separate folder which you synchronized, you simply have to select in the control panel to have that folder synchronized again.
If on the other hand, it is the same install you were using before, and you simply disconnected/uninstalled Ubuntu One, then deleted the folder/files in question, the files may be deleted from the server if you just log in and start syncing again. In this case, I'd recommend running these commands in a terminal:
$: u1sdtool -q
$: pkill -9 ubuntuone
$: mv ~/.local/share/ubuntuone/syncdaemon ~/.local/share/ubuntuone/syncdaemon.old
$: u1sdtool -c
This will stop ubuntuone-syncdaemon, move the metadata out of the way, and restart ubuntuone-syncdaemon and connect. When connected, it should just re-download everything, and if you have any conflicting files in
~/Ubuntu One, or other synchronized folders, create conflict files for them.
If neither of these solutions work, and the files do end up getting deleted from the Web UI view, then ensure the client is fully synchronized with the server (all synchronized folders have the same files and those files are the same in both places), then open a support ticket at https://one.ubuntu.com/help/contact to get more help.