Not very much power is required to illuminate an LED or neon indicator, so excluding faults, it could be just the threshold current of the meter, or induced current from a nearby coil.
If the neutral is connected to the neutral of a different circuit somewhere downstream of the meter, there could be a current in it. This type of connection is bad practice.
There might be a voltage between Neutral and Earth, which is causing it to illuminate.
Whatever the reason, yoe need to contact your Electricity Supplier, and get them to check it out.
I'm sure they'll know exactly what's wrong.
At my home, my Electronic electricity meter shows the Earth leakage and consumption LEDs glow without any consumption. I checked the live wire coming out of the meter and it showed me 0 Amps, but there was current in the Neutral wire. Who could be feeding current into the Neutral wire ? What could be the root cause behind this as my meter is showing consumption without any consumption ?