Ok thanks, I ended up running this command:
sudo unattended-upgrades -d
Like suggested here: https://askubuntu.com/a/412
This took a few minutes, but it finished successfully.
After that the Ubuntu System information displayed the message:
*** System restart required ***
so I rebooted with sudo reboot and now it only shows 1 security update 
199 packages can be updated.
1 update is a security update.