Ok, first upgrade attempt.
Installed a vanilla 1.5.1 on my local LAMP dev server (OS Linux Mint 17.3).
Tested: ok
Then (using Beyond Compare) copied the latest ZC 1.5.5 BETA over to the 1.5.1 installation and deleted all old files. Renamed admin folder back to admin but left the 2 configure.php files read-only.
Then loaded http://192.168.0.20/onefivefiveupgradetest/zc_install (onefivefiveupgradetest is the installation folder)
and was told that there is an old configure.php which needs upgrading first.
Also had the alert that the 2 configure.php files are not writable (as expected), so I made them writable, reloaded and was given the choice to upgrade or do a clean install.
So far so good.
I chose UPGRADE and tick the upgrade steps (all), entered the admin credentials and proceeded.
Within a flash I was greeted with
Setup Finshed
Congratulations, your upgrade is now complete.
You need to remove the /zc_install/ folder so that someone can't re-install your shop again and wipe out your database! A message will appear and you will not be able to log into your admin until the folder has been removed.
So, did as told and removed the zc_install folder, then reloaded http://192.168.0.20/onefivefiveupgradetest/ - result ok.
Then loaded http://192.168.0.20/onefivefiveupgradetest/admin-test/ and got this:

The interesting bit is that the address jumps from http:// to https:// and I did not enable SSL during the installation or upgrade procedure. So naturally that screen must display (the server works as expected.....)
Renamed the admin folder again to something simpler and got the same screen.
So I searched the DB for 'SSL' and in the table configuration I found these entries:
configuration_key SSLPWSTATUSCHECK was set with configuration_title 'login mode https' - manually changed that to 'login mode http' and reloaded the admin: Bingo, the admin login page appears. Tried to log into admin and get the same screen as above. The address is again https:// ..... :huh:
Also noted that the admin folder was not automatically renamed as it happend during a fresh install.
So, it seems that there is still some work to be done to get an upgrade from a vanilla install working smoothly. I do understand that my scenario is not a typical scenario as most sites have been customized before upgrading. But it should work smoothly with an upgrade from a vanilla 1.5.1 installation - so me thinks.
Other than that last bit everything went smooth as - thumbs up!! :cheers: