You can be very sure the design and manufacture of both gas and electric meters are very closely managed, and each meter will be calibrated finely before it leaves the manufacturer. The standards applied to these are quite strict, and because of weights an measures.
It is certainly possible that an official meter is inaccurate, and there have been verified reports of where a meter has been over recording energy usage, but its very rare, and I doubt any plug in meter reading would be taken as a reliable evidence of over charging, but it might be corroborative evidence to trigger a calibration check by the power company.
Modern life now seems to revolve around masses of electronics and technology. So many appliances you buy these days need power, and may come with "Wall Wart" or plug in power supplies.
It can be a wake up call if you were to accurately check the amount of power some appliances or their power supplies actually consume even when "Turned Off" USB or phone chargers for example if they feel warm to teh touch when they've been disconnected for more than 30 min, then its fair bet they're actually consuming a few watts of energy.
Now if they are in a room hat being used, then the waste heat is not actually being wasted, its helping to heat the room, but if its in a bedroom or a garage or any other normally cooler room, those watts of power are being wasted, and it's costing you money. The obvious thing is to unplug them when they're not being used, but often the sockets are inaccessible so they're left plugged in and turned on.
Our cat prefers to drink moving water, and my wife decided to get a water fountain for him. This stood in the corner continually running its small AC motor driven pump from a plug in transformer. I noticed how warm the transformer was, so I measure its power consumption, and it was continually drawing 10W. in five days that over 1kWh of energy. I had a spare infraRed motion detector from an old flood light, and I have set that up to trigger the pump only when the cat comes near. The transformer no longer gets warm.
I also had an electric kettle (from ALDI) which had temperature settings from 40C to 100C. This was useful for a variety of purposes such as only heating water to 70C for hot water bottles or 90C to prevent it scalding coffee beans etc. But I discovered that when its on its base and even when not heating its consumed about 7W. Our electricity supplier had supplier several years ago had distributed a number of power saving devices, and one of them was a plug in 30min timer. I now use this with the kettle so it's really off now most of the day.
Other devices like a multiway socket strip which has one designated "master" 13A socket and a number of "Slave" sockets, and the slaves are only powered when the appliance plugged into the master socket is turned on and drawing power. These are great for things like TV and ancillaries like DVD players, Computers and monitor or routers, printers etc, and so on Hi-Fi.
Another solution is to use smart plugs which can be linked to WI FI or separate radio controlled switching, for things like lighting or even power device like heaters.
One of the surprises many people have when they look at power usage is how much is used on lighting. LED lighting is definitely far more efficient than older technologies but even so lighting is often used for long periods, and that means even the meager power usage adds up.