It's Radio 4 actually ! Indeed, if used, the Radio timeswitch or Teleswitch switches the Economy 7 (or other cheap tariff) supply on and tells the meter to start recording at the cheaper rate.
This can also be done with other types of meter which have an in-built clock which switches a contactor or relay on for the cheap rate period.
Basically yes, your storage heaters will be wired in such a way that they only receive power for 7 hours at the cheap rate. It can be a different part of the meter or a seperate circuit fed from the same meter via a timeswitch as described above. All depends on what type of meter is fitted, when it was installed, how it was wired etc.
Hope that helps.