My iMac has downloaded and started the install of Big Sur from High Sierra, it starts with 29 minutes remaining, gets down to ‘under a minute remaining’ then never changes, I’ve tried it several times, leaving it over night and for 24 hours, help!

You need at minimum, 35.5 GB of available storage on your iMac before you can commence the Big Sur upgrade from High Sierra, and a 2014 or later model iMac. If it is running out of space during the installation, then it might behave as you describe. Free up the appropriate measure of storage, uninstall any anti-virus product that you may have running, reboot the iMac, and again, attempt the Big Sur upgrade.

Shutdown the computer by any means including the Power Button. Disconnect all external devices. If a laptop - connect to charger and wall socket for power.

Restart and Immediately hold the Shift key and keep holding until the Apple Logo is presented. This will be Safe Mode which doe a Repair Disk, clears cache files and only loads Apple Software, extensions and fonts - loads slowly - Normal.

The above may or may not allow the upgrade process to complete - hopefully successfully.