You’re correct: **in a correctly wired, healthy circuit, opening just the live wire stops current through both the appliance and its neutral wire.** A single-pole switch is therefore sufficient for ordinary on/off control, and is widely used.

The advantage of a double-pole switch is **disconnecting the appliance from both supply conductors**, which matters when something is wrong:

- **Live and neutral are reversed:** A single-pole switch may then open the actual neutral. The appliance stops working, but its internal wiring remains connected to live. Touching it while grounded can complete a new circuit through your body. A double-pole switch disconnects both wires regardless of their orientation.
- **Neutral becomes hazardous:** Neutral is normally close to earth potential, but wiring faults—such as a broken upstream neutral—can raise its voltage. Opening only live leaves the appliance connected to that neutral. [Electrical Safety First’s isolation guidance](https://www.electricalsafetyfirst.org.uk/media/1201/best-practice-guide-2-issue-3.pdf) discusses circumstances in which neutral can become live.

The key distinction is that **“no current is flowing” does not mean “no dangerous voltage is present.”** Current needs a complete path; touching a connected conductor can create that path.

So a single-pole switch can be used where ordinary switching is sufficient. A double-pole switch provides more complete disconnection where isolation is required. For maintenance, the device must also be suitable for isolation, and the circuit must be verified dead before work. [HSE guidance](https://www.hse.gov.uk/electricity/maintenance/isolate.htm)