Electronic – Testing UK carbon monoxide power socket is live

Sounds like capacitors to me. Since the multimeter is most likely verifying continuity with a DC supply, an uncharged capacitor will appear like a short for a brief moment.

Also found this at https://learn.sparkfun.com/tutorials/how-to-use-a-multimeter/continuity:

Continuity and large capacitors: During normal troubleshooting. you will be probing for continuity between ground and the VCC rail. This is a good sanity check before powering up a prototype to make sure there is not a short on the power system. But don’t be surprised if you hear a short ‘beep!’ when probing. This is because there is often significant amounts of capacitance on the power system. The multimeter is looking for very low resistance to see if two points are connected. Capacitors will act like a short for a split second until they fill up with energy, and then act like an open connection. Therefore, you will hear a short beep and then nothing. That’s OK, it’s just the caps charging up.

You get voltage reading because it's AC, so it passes through air as through a capacitor, it means nothing. As for grounding, be careful, don't kill anyone with that neutral wire. Ground the cases and enclosures of your equipment and use earth leakage circuit breaker. Neutral may hold voltage by itself (referenced to earth).

Edit: it's residual current circuit breaker, apparently.