How to disable BIOS update feature in Ubuntu 17.10/18.04?

The software responsible for this type of update is fwupd.

fwupd is a simple daemon to allow session software to update device firmware on your local machine. It's designed for desktops, but this project is also usable on phones, tablets and on headless servers. You can either use a GUI software manager like GNOME Software to view and apply updates, the command-line tool or the system D-Bus interface directly.

To get rid of the updates you can uninstall fwupd easily:

sudo apt-get remove fwupd

^(Source)

Stop the service, disable automatic start upon boot, and disable manual invoking with:

sudo systemctl stop fwupd.service
sudo systemctl disable fwupd.service
sudo systemctl mask fwupd.service