I did the same for somebody.
He replaced the storage heaters for some gel filled panel heaters that were made to look like wet central heating radiators, I think they were French.
They are all radio controlled by a central timer, and each has a thermostat.
My customer is happy with them, and swears it's cheaper than the old storage heaters were. Personally I'm not convinced.
BUT, (and there's always a but) he not only kept an off peak tariff, he converted to Economy 10. As well as the 7 hours overnight at the cheap rate, you get 3 hours in the day at the cheap rate. So some of your electric heating is still at the cheap rate, and don't forget you still get a tank of hot water each night at the cheap rate.
All I did was swap the off peak CU over to the unswitched feed, so it's live 24/7 for the heaters, and put the immersion heater on a timer for the overnight cheap rate, and the mid day cheap rate boost.
Have a look at what tariff your customer is on. If it's Total Control (a preserved tariff no longer available to new customers) then keep it, as that lets you have cheap rate for panel heaters at any time of day. If you have that tariff, you most definitely want to keep it.
In my last house, I kept the E7 even after replacing the storage heaters for central heating. It was worth it just to have the washing machine and dishwasher operating overnight on the cheap rate.
Like others I think your customer is making a big mistake. I would suggest before dumping the storage heaters, she try it for a month just turning off the storage heaters and using plug in electric panel heaters. I'm willing to bet she won't like the house being cold most of the time, and won't actually save much if anything.