Maybe. Such meters clearly still exist, as witness the couple of links to manufacturers that were posted. However, that does not, in itself mean that they are currently 'readily available'. Supply problems arise. As you will be aware, there are currently some serious 'availability' issues related to certain hormone-based medicines, but they certainly still 'exist'.Although we hardly use the storage heaters, having E7 still saves a little bit. But the point is that new meters providing the OP's switching requirements are clearly still available, and the supplier is just being lazy in pretending they aren't.
The days of tariffs such as E7 are presumably numbered, and the attractiveness of them has already diminished. Following a period of many years in which the financial advantage of E7 (for some) had remained essentially unchanged, a couple of years ago most suppliers moved their 'night' rate to much closer to the 'day rate', presumably as a consequence of changing patterns of demand during the day/night. As the below illustrates, in my case, that resulted in the saving resulting from E7 (without storage heaters - but I'm unusual in my pattern of electricity usage!) reduced from £250-£350 per year to only about £100-£150 per year. Last April, I partially reversed that by finding one of the few suppliers that was still offering reasonably attractive E7 rates, but my saving is still less than it was a couple of years ago ....
We can only guess about what is going to happen with electricity tariffs in the future. If the planned explosion of electrical vehicles happens, with vast amounts of night-time charging, the present situation could reverse, with the lower electricity demand (hence potentially cheaper electricity) being during the day, rather than the night - and, if it doesn't quite reverse, the major difference between day and night could largely disappear. Furthermore, as I have already mentioned, if the 'smart meter' system ever gets going properly, we'll then presumably eventually see multiple changes, potentially dynamically (hence possibly unprdictably), in electricity prices during the 24 hours, so goodness knows how either humans or technology would then decide when to 'power up' on the likes of storage heaters!
Yes, that change has been a pain. It is allegedly a 'safety feature', so that appliances don't spring into life, maybe when unattended, when power is restored after a power cut - but that seems to be a fairly lame explanation/excuse, given that many of the appliances have built-in timers specifically designed to allow them to come on 'when unattended'!Over time replacement units usually no longer reset simply by turning on the electricity supply, so we have to rely on their own internal timers. That is annoying because power cuts usually of only a few seconds are commonplace, but cause modern appliances to lose their settings.
Kind Regards, John