Up to you really. The main thing is to avoid leaving a cut end sticking right up where you can see it.
If there are leaves on the flower spike and you want to keep those, take it down to where the leaf joins the stem. If the flower spike is branched and there are flowers on another branch that haven't finished yet, you can take the finished one back to the branch point. Or leave the whole spike until all the flowers are over. Or you can follow the flower spike right down to where it's coming from the main plant and cut it off there.
Doncaster, South Yorkshire. Soil type: sandy, well-drained
My problem is, I'm distracted by the cricket . Also, I have always had a problem with cordyline/phormium id. I have a mental block where they're concerned.
Edited to add, I have just realised you may have thought I was being sarcastic Hostafan, that wasn't the case, I just realised you were right and I hadn't twigged.....
I know they're hugely popular with many, but I'm a fan of neither. They're so often scruffy and full of dead foliage, and many have had hideous "haircuts"
I don't like them myself. My experience is with helping my sister to get her four humungous purple-leaved phormiums in order after the previous owners had given them very bad haircuts (leaves chopped off halfway down) and left lots of dead leaves and old flower spikes in them.
Doncaster, South Yorkshire. Soil type: sandy, well-drained
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Edited to add, I have just realised you may have thought I was being sarcastic Hostafan, that wasn't the case, I just realised you were right and I hadn't twigged.....