Replacing old electric heating system

I just bought a new place for my Mum (fairly large 2 bedroom flat). It has an electric immersion hot water heater as well as very, very old electric storage heaters (radiators) from like the 1970s throughout the apartment. It is absolutely swallowing money, whilst not offering much in return (hot water doesn't last long, radiators switched off to save money but still doesn't seem to do much).


I am wondering what the best option is to sort this is (assuming I stay with electric heating). I (sort of) have had 2 opinions and am wondering what people on here think.


Any ideas? I would consider gas, but it seems like the installation costs would be huge...

We had our heating and cooling replaced yesterday and I have to tell you these guys https://titanupgrades.com/services/insulation/ were very nice and oh so quick. I can recommend these people.