You are running a custom ROM, so it's certainly rooted. Updating SU will not change that. You will need to find the appropriate ROM Update Utility for the phone. This depends on whether it was sold unbranded or with network software on it. If you know this it would help, but it sounds like you bought it second hand with a custom ROM.
Could you shut the phone down, then power up while pressing the volume down key? That will take you to a white screen with a little menu on it. Tell us everything it says in the top few lines of the screen.
(When you've done that, there's a reboot option, either on that screen or the one you get by selecting the "fastboot" option from the menu).
An RUU will wipe the phone, so yes, a backup is a good idea.
Thom, as topgazza's location is "UK" it's the International All Things Root forum that you need.