Economy 10?

A DD increase of that scale is nothing to do with price increases. It is almost certainly because they have not been submitting regular reads, their bills have been estimated, and now following an actual read, they have received a big catch up bill, with a consequent hike in the DD.
First thing to do is check the last bill against the meters. if it's not based on actual reads, submit them at once and get an accurate rebilling. Then submit reads at least every quarter.
AFAIK, there is no such thing as a telefoto meter. Do you mean a teleswitched meter? These switch between night and day rate by picking up a radio signal, hence the name. The older E7 meters are switched by means of a built in clockwork mechanism, which is often innaccurate.
They are not on E10 unless they also receive a 3 hour cheap rate period during the day. Check their bill, it should be obvious if it's E7 or E10 by the name.
Every provider offers E7, and a switch is easily done via a comparison site: you just need their postcode and the annual kWh usage figures on each register. Only a few providers offer E10, and any attempt to switch away from the legacy provider without new metering is likely to end in tears. Because of their limited availability, they do no tappear on the comp sites either.

With no gas there will not really be any other cheaper options for heating. Firstly make sure that the registers are being billed the right way round, it is surprising how many are not resulting in large bills. You need to find their annual kWh consumption on each register and look at switching. Not all suppliers support E10, some will support it completely, some will take it on as E7 and some not at all. None of the comparison sites will show it so you will have to do some work calculating the cost. It may also be worth switching to an E7 meter which will completely open up the market to them but they will lose that afternoon boost. Start your research here https://economy10.com/overview/list-of-suppliers/

molerat's advice is spot on. Forget about switching fuels: you have already said that gas is not an option. Get hold of the recent bills and reads and do as suggested. Such an increase in DD can only be due to a catch up bill, a misread, or (very rarely) a faulty meter.
E10 does give you fewer switching options, but it can be good for a property occupied all day.
Are they perhaps using other forms of electric heating as well as NSH's during day-rate hours? If so, this usage will be at peak rate.

The company is Economy7 energy, they take on E10 also.

Look switching E10 suppliers for a better deal is never a success. Tiny and wholly uncompetitive market support means they all charge fractionally the same.

E10=10 hours of cheaper - E7=7 hours of cheaper.
Most suppliers will swap to the much cheaper E7 without the need for a meter change, they simply total both day/night counters and average them for billing.

99% of all UK meters are tele-meters. The 3 daytime hours is the 'boost' not the other way round. £2400pa is three times my consumption and double the average, I too am NSCH and all electric.

Online account will give the O/P stats including the 'tariff' discounts meter reads seasonal use and the critical kWh per annum. kWh is the tool to understanding the A/P's actual real-time use.

Knowing how to even use night store heating effectively is something many many people have not one clue about. So tariff, online best deal, regular meter reads per month, stop or reduce day use or install and extra NStoreH in the living area and go to E7. The more storage of cheaper [30%] night heat the less less use of the expensive day and a much safer and "comfortable" the AP's will be.