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PeterS
I can't zoom in to read the meter details clearly but it looks to me like the meter is a standard four wire meter, connected via a two pole isolator switch (because the distance between the meter itself and the consumer unit is more than 2 metres distance) to the consumer unit. In this instance, it doesn't look like you have any external timeclock, RTS controller or anything out of the ordinary.
It looks to me like the meter itself is potentially a smart meter but has a blanking cover fitted where the smart communications hub would normally be installed. Obviously without that hub, the meter can't work as smart.
Now, either you live in an area where there is no communications so the hub couldn't be fitted thus making it a bit of a pointless exercise or the meter installer has installed the new meter, updated the MPAN data on the database and that is showing up to E.On Next as being a smart meter and therefore they can't fit a replacement as they think you already have a smart meter.
Was this meter installed by a previous supplier or has this been done since you have been with E.On Next?
I'm also guessing that your property is fairly small as the main incoming fuse is only 60A so any complex heating system would be pretty small...just a hot water tank and two or three storage heaters, maybe?
The tariff you are on is conditional on having a smart meter fitted 'where eligible' and if they cannot, or don't want to, fit a smart meter, then that should be their problem, not yours. That tariff ends this spring anyway so whether or not they plan to extend the scheme or put a similar one in place next winter, I cannot say.
The sticker on the meter says SSC, which I think is Scottish and Southern Contracting. Only Scottish and Southern regional areas, back in the days of Heatsave and Flexiheat used complex metering systems as a legacy of the old Magnox nuclear days when off-peak electricity was cheap and they were pushing 'all electric' heating options. That is why SSE exist today (as part of OVO now) , as a merger of two geographically separate areas who both had a lot of these legacy systems which didn't exist in other regions.