Best answer by Tim_OVO
That doesn't sound right,
The lights and the sockets are connected to the mains power via the meter. If the lights are one, the meter will be working. I'm not sure about those sockets, but if you're in any doubt about your meter, press A, A, B on the keypad to wake it up and look at the meter display for signs of life.
Anyone else had a similar thing happen following a power cut
This is for next time there's a power cut: https://www.ovoenergy.com/guides/energy-guides/what-to-do-in-a-power-cut.html.