If the failure is just "do not arm APP" or something like that, you can fly the ILS anyway you want: manual/FDs off or LNAV/VNAV or HDG select / V/S. As long as you follow the raw data obviously and is prepared to intervene or go around.
Just remember to raise the minimums to raw data minimums, if necessary, as you no longer have ILS FD guidance. 750 meter RVR instead of 550, But not sure if that is EU ops or my company SOP (too lazy to look it up).
Personally I would just click it out and switch the FDs off, 750 meter RVR is a lower minimum than the VOR in any case.