Economy 7 is a tariff, it started with the White meter and a completely independent fuse box, this was before the consumer unit had been invented, the problem was everything else, even during the 7 hours of off-peak, was still supplied with peak priced electric, so a number of improvements have been made over the years, from twin immersion heaters and special timers, to using a trigger supply to turn on items during the off-peak, and supply all with the off-peak supply.
Even the smart meter, can have a dual output, or rely on the user to set timers, mine relies on me to set timers, on washing machine, tumble drier, dishwasher, immersion heater, and battery.
So RDS turn off, may affect all, and it may have no effect, it depends on how it has been set up, and what signals are sent before it is turned off, since the user has nothing he can do, it seems pointless telling people what is going on, the only thing which the user can do is accept or reject a smart meter, and to have off-peak he/she has to accept the smart meter. Otherwise, you can't have an off-peak supply.
Where I live, with Octopus, with no off-peak it costs 23.86p/kWh, with the off-peak I have selected it cost 8.5p/kWh for 5 hours 00:30 to 05:30 and 30.17p/kWh rest of the time, they also pay me 15p/kWh for export, so I charge out batteries with off-peak, so use very little peak power.
But there are a whole host of tariffs, some with three stages and only 3 hours off-peak, some, where you give the supplier control of when your battery charges and discharges, some with 7 hours, some with 10 hours, some change every ½ hour, I noted one where peak tariff was 39.9p/kWh, so one has to be careful to select the one that suits you.
Also, standing charges change tariff to tariff. Personally I wanted to select and forget, once done, that was it, many you are locked into for 12 months, but with an off-peak tariff you need to have something which uses it, be it solar, EV charging, storage radiator, and since the suppliers offer different deals area to area, it is no good, for someone outside your area trying to advise, seems Ulster is very bad with tariffs offered.
It is unlikely there is any problem with Smart meters and loss of RTS in London, the problem is where Smart meters will not work, mainly Wales and the North above the Liverpool - Hull divide

there has been nothing I have seen which says what will be done if the Smart meter will not work, over the years the power suppliers have changed their mind many times, we all remember creature comforts

with off and on-able. Seems odd now, where gas is controlled with up/down and on/off is seen as bad and old-fashioned.
But the suppliers have known for years there are no replacement valves for the BBC long wave radio 4 transmitter, so at some point it will be turned off, but it seems they think by magic a new valve will be found, but nothing the user can do.