The light fitting with the bulb in it will have Live currants (coming in from the switch) and Neutral going out to join the main lighting circuit.
So there is a Neutral but not in that particular part of the ensemble, it is for the 'used' currants after they are burnt in the bulb to make light .
Live --> switch --> bulb --> Neutral.
As noted above, exact details will vary depending on whether it is a single switch, a paired switch (like top/bottom of stairs), off to the side of the wires going to the light, or on the way...
Oblig. Disclaimer

Especially if my umpteen rewrites mangled the logic and made it all the wrong way round

Neutral can zap you just like Live does.
Always be careful when deciding something must surely be 'neutral', remember that this does not mean no voltage on it, switch off the circuit before opening anything, and use a voltmeter or a volt-detector anyway but check those work before trusting your life to them

If in doubt, get it done by a mate who says he did a bit of that wiring malarkey once.