We also have storage heaters here, but the running costs are quite reasonable. (In line with gas prices.)
But then we do also have a well insulated concrete house.
Still working on improving the insulation mind you.
I would hazard a guess that changing your heating system isn't going to save you any money, but improving your insulation situation is most likely to help.
As such some questions:
Do you close your window air vents in the winter ?
(I tend to leave one open at the top of the house to allow airflow, and one open at the bottom, whilst in summer, open them all!)
Do all your doors and windows fit well with no draughts ?
(Our front door needed quite a lot of work to make it fit, as the frame wasn't installed level and we had a huge gap at the top !)
(I'm also working my way around the house filling in and painting all the gaps around the window frames.)
Thick lined curtains help. (I hear almost as good as double glazing.)
(Still got to fit one on the front door.)
Thick carpets and underlay can help. (Recently put carpet tiles down in several rooms such as the kitchen to help there.)
(Got the cooker extractor to work on, fitting a one way valve to stop the wind whistling in!)
As such in the last year of improvements, heating costs have dropped some 25%. (I reckon there is perhaps another 10%+ improvements possible here.)
Outside, if possible wind brakes to stop the heat being taken away from the building, ideally trees/bushes, but stone walls/big stones at bottom of house, earth banks can help too.
Our house also has outside insulation, which is better than inside, as then the thermal mass of the building can act like a giant storage heater itself and help maintain a steady temperature more easily.
(I'd be wary of cavity wall insulation, as that can cause damp issues.)
One could make further improvements such as a heat exchanger for incoming/outgoing air, but whether that would be cost effective or not, I don't know.
(I plan on that for my next home though, as I'd like a air heating system, but that would require duct work, and not necessarily be cheap to run, so would only go for that once I've my own generation solutions in hand, eg. solar/wind.)
If you don't mind me asking, do you keep a log of your electricity consumption ?
(Ideally heating usage marked separate.)
If so, can you share any figures on your usage.
It might be useful to check your Immersion/hot water heater settings, how many hours a day does that come on, and what temperature setting is it at ?
Enough insulation around the cylinder ?
I found with ours it was difficult to find any instructions for the controller and took quite a while to figure out how to set it correctly to only come on 3 hours a day. (2 of which during cheap electricity rates.)
And the temperature setting was a bit too high, so when it was on, it was on and almost boiling away !
Storage heaters might be a bit blocked with dust.
Ours also came with a fan assistance temperature controller on the wall (No one seemed to know what it was!), but I find that isn't really necessary here, so that's turned off.
I usually have our old storage heaters set at 50% heat output on average, turning the biggest heaters up to around 80% when it gets really cold, and off totally in the warmer months.
(We have two large, and 3 small, but generally don't need the 2 small ones on.)
Do you live in a wooden structure ?
(Harder to keep warm, if you could increase the thermal mass in the property, that can help.)
Hopefully some of that is useful to you.