Having a separate "white meter", E7 (or E10) circuit was normal when these off peak tariffs were first rolled out, as the intention was to use the excess electricity generation capacity at night to run heating and hot water systems. At the time, a lot of UK generation was coal fired and nuclear, and couldn't just be shut down at night, so this was a way of being able to increase night time demand.
Newer E7 installations don't use a teleswitch, but use a clock in the meter. This has the ability to control a remote contactor, so if needed a secondary off-peak circuit can still be used. This system works the other way around, though. The older systems used the teleswitch to both turn on the off-peak circuit and signal to the meter to change rates. Newer E7 meters have the signal to switch to the off-peak rate generated by the meter.
The teleswitch system is virtually obsolete, as they haven't been fitted in new installations for a few decades now. Also, long wave BBC Radio 4 (used to transmit the teleswitch code) is hanging on by a thread, as it relies on a small stock of obsolete transmitter valves, and when these are used up it will have to either switch off, or operate at a very much reduced power level, using a different transmitter.
We had an E7 meter fitted a year ago, it was done about a week after I requested it, by SSE. We don't have a separate E7 only switched circuit, but rely on time switches to switch things like the water heating boost and car charge point on during the off-peak period. I prefer to have the charge point controlling the off-peak charge period, as it's a much simpler way to do things, rather than have to change the settings in the car. Mind you, the BMW i3 off-peak charging is very weird, and only works if a departure time is programmed, and if you don't then depart at the set time the car bleats at you for not having done as you've said you would. Typically Teutonic, I guess...