I would also be cautious about whether what you have is actually true 'Economy 7'. That's about the closest matching scheme that the energy companies have that matches your system but RTS was a bit more clever than that with the older 'complex' heating systems like yours.
E7 is a 'straightforward' setup where you pay day rate for electricity for 17 hours a day, and get 7 off-peak hours. The off peak period is usually between midnight and 7am but this can vary according to which supply region you are in.
Radio Teleswitch System didn't rely on a meter or time-switch to determine peak and off-peak hours, but could send a signal to the RTS unit to give you cheaper electricity based on local demand and also give you an hour or two of cheaper 'boost' off-peak power to top up the heaters during the day in cold weather, or at weekends when industrial and commercial loads were lower.
Some of the older 'complex tariffs' even had four rates. Peak and off-peak for the general household electricity, and another two peak and off-peak prices purely for the heating.
You should see two rates and E7 on your tariff if they do have you on E7, but you'll possibly not get a straight 7 hours seven days a week because of the way the RTS box physically switches your meter rates.
A standard 5 terminal Economy 7 smart meter should work fine, but you may lose a daytime 'boost' function on your immersion or storage heaters if that is how your system is currently configured. The only way to know that, without getting an electrician in, is to see what happens when they swap the meter. Fingers crossed, all will be well.
My colleague @meldrewreborn is rather good at drilling down into the numbers and getting to the root of billing calculations/errors and putting together suggestions for moving issues forward. I'm more an 'on the tools' bloke with a bit more experience of the technical side of domestic and commercial installations. Unfortunately, neither of us are on the payroll of E.On Next and their 'energy experts' don't have the background or experience with some of the more 'interesting' problems that occasionally crop up. It is hoped that our advice doesn't fall on deaf ears and that if nothing else, we can at least provide community members with some 'ammunition' when they have to go 'toe to toe' with the supplier.
Good luck with the meter exchange, and keep us posted as to any developments. Any problems, we'll do our best to assist 👍
Don't shoot me, I'm only the piano player. I DON'T work for or on behalf of EON.Next, but am willing to try and help if I can. Not on mains gas, mobile network or mains drainage. House heated almost entirely by baby dragons.