Can't activate secure boot after upgrading from Win 7 to Win 8 on a Spectre XT

Hi everybody, I'm struggling with the UEFI of my brand new notebook, and after wasting some time with the HP support, I found this great forum which you've got here.
Therefore, here goes, I'm reposting the very same question which got no useful answers from HP. Many thanks in advance for any ideas!!!

The PC I recently purchased is a Spectre XT 13-2005tu (i7 processor, 4Gb RAM, 256Gb SSD) with Windows 7 pre-installed.
After installing my favourite applications and using it for a few weeks without any trouble, I thought to take the opportunity of the $14.99 upgrade to Win 8, so I downloaded Windows 8 Pro and installed it (as an upgrade, rather than a fresh installation, because I didn't want to loose the customizations I already made).
I also installed all the updates available on HP website (sp59158 for updated BIOS, sp58404 for UEFI support, ecc.)
The whole upgrade worked nicely, and the PC is now up and running with Win 8.

Now, I'm trying to use at best all the possibilities Win 8 has to offer, and among them, the UEFI secure boot.
I found the "legacy support" option in the BIOS settings, which as I understand must be disabled to activate the UEFI secure boot, but if I do that the PC tells that there's no operating system on the disk and doesn't boot anymore.
Which was a bit scary by the way, but eventually I could re-enable the legacy support in the BIOS and have the PC working again, but of course with no secure boot.

I suppose there must be some other re-configuration that should be done before changing the BIOS parameter, but I couldn't find any instruction for that anywhere on the web.
On the other hand, it would be indeed weird if the secure boot could not be configured AFTER the OS upgrade, and a new fresh installation would be necessary.
I'd rather part with the secure boot than re-install everything, but that would be a shame...