Should I be offered the option to upgrade to 18.04.1?

The upgrade from 16.04 LTS to 18.04 LTS does not occur until the .1 release has been out. The usual procedure is the 'taps' are turned on a few days after the .1 release. Currently we're only hours after the release, not 'days', so the update will not be offered quite yet.

It's mentioned in the release notes:

"Users of Ubuntu 16.04 will soon be offered an automatic upgrade to 18.04.1 via Update Manager."

-- update 2018-08-08 ~04:30 UST/UTC

It may soon be available; if this is the 'critical' bug holding up release (https://bugs.launchpad.net/ubuntu/+source/gnome-menus/+bug/1766890) - it only impacts 16.04 LTS -> 18.04 LTS upgrades. 18.04.1 is stable; it's the upgrade-path that is turned-off..

-- update 2018-08-10 ~10:10 UST/UTC

https://lists.ubuntu.com/archives/ubuntu-release/2018-August/004556.html

"We are working on resolving bug http://launchpad.net/bugs/1766890 which results in a bad upgrade experience when people upgrade to Ubuntu 18.04. There is a new version of the dist-upgrader in -proposed and we will be testing it the next couple of days and plan on updating meta-release-lts at the beginning of next week."

For anyone still receiving the "No release found" error several days after 18.04.1, this process worked for me to upgrade from 16.04.5 to 18.04.1:

Software & Updates > Updates > Notify me of a new Ubuntu Version > Select "For Any New Version" > Open Software Updater

For some reason, "For long-term support versions" was not notifying me about 18.04.1 LTS.

Once I changed it to "For any new version" I was immediately prompted to upgrade to 18.04.1. The upgrade has run without issue.

Mahalo to deadflowr for originally suggesting this fix here: https://ubuntuforums.org/showthread.php?t=2397703