I don't know what part of the UK you're in, you haven't said, but even here in London, these plants are susceptible to damage during winter - it seems that this year we're in for a worse one than last year, so plan to move your cordyline somewhere frost free if possible. If you can do that, then cut back now, but this is really best left till Spring, as is repotting, when the growing season begins. Cut back now if there are signs of problems other than the leaves dropping off that stem (its soggy, weeping, damaged, etc.) and repot now only if roots are literally packed and hanging out the bottom.

I have cut back all stems with rotted tips. It saves losing the whole plant.
If there is going to be a harsh winter Sheringhams Cords are going to die.

Many thanks for your answers. Very much appreciated.Thank you for taking the time to answer my question.