Hello OP. I am also in an electric flat without storage heaters and it seems I use much less electricity than you. As others have suggested, checking your meter is actually monitoring your flat and is doing so correctly is the first port of call.
Then, a possibility to save on heating is a heated electric blanket for use on the sofa. If your wife needs to be much warmer than the ambient needs to be, you could get away with a much cooler temperature and she might be warm enough. If so, the savings may be enough and save the need for more up front expensive solutions.
Meter sanity check was done and my meter seems to be the correct one as when I switch off the consumer unit my meter reacts momentarily and the serial number on the meter is the same as on my bill.
Electric blanket was indeed bought a month ago - best purchase I have made in my life - every resident in an old building must have one for sure.
Don't know anyone offering E10 metering to new users. Most of the new - and many now failed - suppliers didn't have to support it - and most of the big boys - its a legacy customer only option.
Some like EDF do still publish the rates every Ofgem cap rise. See links at bottom of their EPG guide page. And saw one post - saying being offered a different rate recently - to take over an old SP E10 customer.
Dropping E10 now seems perverse now they are paying others to avoid usage at say 6pm - on mainly low wind days it would appear.
My E10 hours - winter - midnight to 5am, 1pm-4pm, 8pm-10pm.
So makes it a no brainer for me to do washing or cook early late - some days - particularly at weekends - and avoid peak time.
There were iirc c4m on multirate meters - 0.5m of them on non E7 - so legacy E10 / telemetry IIRC - in an Ofgem 2021 data report.
High HRP panels like Dimplex Quantums and others by other brands - can be wired only to 24/7 live circuits - you just have to make sure the programmed timing is correct - but they are not cheap as simple heat panels / some radiators.
You don't need split wiring to be on an E7 tariff - it's just a tariff.
But as others - guessing first start point is checking what sort of E7 tariffs available in your region.
Some people managed to have E7 work for them - without storage heating - but some are now looking to switch.
As to how many HHR panels you would have to fit - to use enough to gain vs SR - comes back to regional / supplier dependent E7 splits.
Seen ranges quoted pre post Jan changes from
c30% to over 50% for % night - to beat SR EPG. Most all suppliers offer different rices - it's not like single rate.
Then get a quote - including or just installation - start with the living room - as that will I guess be most of the hours of the day (e.g. 16 of 24 - and probably the biggest room) . As a new installation mod - your almost certainly going to need an electrician anyway.
Then main bedroom.
Option 3
Do too many panels - and touching on air source type price you quoted in post - but then that leaves you with the leaseholding company ?
Have you enquired - just provisionally - what they would or would not allow ?
They may have even been asked by others in the same or similar position in recent months.
Replies
Then, a possibility to save on heating is a heated electric blanket for use on the sofa. If your wife needs to be much warmer than the ambient needs to be, you could get away with a much cooler temperature and she might be warm enough. If so, the savings may be enough and save the need for more up front expensive solutions.
Electric blanket was indeed bought a month ago - best purchase I have made in my life - every resident in an old building must have one for sure.