The old meter will at some point need changing, as the radio 4 LW time signal is due to end. But economy 7 is a tariff, not a system, and over the years the way it is used has changed.
In the beginning, we had white meters, and a completely different fuse box for off-peak and on peak supplies. But this did not allow the use of washing machines, tumble driers, and dishwashers at night, and for the immersion heater often one had different elements for peak and off-peak, so you could not heat up enough water for a bath during the day.
So it was latter combined, so all went peak or off-peak, and often a signal was used to tell the storage heaters when to charge. So today my off-peak supply is from midnight to 5 am, and my solar panel inverter is set to charge my battery from 1 am to 5 am, as not sure if midnight UTC or BST so 4 hours is enough anyway.
The peak and off-peak is now done with the smart meter, and my peak rate went up a few p, and the standing charge went down a few p, and the off-peak is down to 8.95p per kWh. Even without my solar panels and battery, the cost difference between the two would be rather small, looking at my app on the smart meter, 6th July 2024 used 0.31 kWh, or £0.10 with standing charge £0.69.
The in home display (IHD)
advertised by the Freddy Boswell look alike, is near useless. But my washing machine, dishwasher, and tumble drier all have a delay start built in, and these are the heavy power users in the home. So even without solar panels and battery, setting these to run off-peak, likely the power will cost less than having a single tariff.
Of course, you want good quality when running overnight, not sure if I would want a vented drier running overnight, but the heat pump type should be OK. With of course a smoke alarm.
But if you have a white meter still, better to get it changed now, rather than wait until radio 4 LW is turned off.