Saving energy in general is a positive step. For example, we've just bought a new freezer and dishwasher with better energy ratings and these will save money over their lifetimes. However, when is the best time to run a wash to save the most CO2e?
Unless you are on an Economy 7 style tariff or have solar panels then when you use power has no effect on how much it costs you. If you are, then at night or in the middle of the day is better, respectively. Dynamic demand to grid signals isn't ready for consumer adoption yet but you can look at the information manually if you want to use power at less demanding times.
The grid frequency is a reasonable indicator but is pretty technical. There are other, easier to understand, data sources available:
- Earth Notes: GB Grid Intensity gives a simple traffic light indication
- GridCarbon is a real-time carbon intensity app (CO2 Modeller is from the same guys)
- MyGridGB shows similar data on the web (and includes Solar data)
By avoiding peak time you may not save money but you can save carbon.