Replacing my existing storage heaters with new and hopefully more efficient ones!

I too have Quantum storage heaters running on an Economy 7 tariff. Of course, there are many variants of heater model and wiring arrangement, so it’s difficult to make concrete suggestions.

I suspect that your second Consumer Unit (the current name for what we used to call fusebox) is connected to the fifth terminal on your meter, which should then be configured to switch on and off according to your Economy 7 hours. But from what I can make out from the Dimplex documentation, it’s possible to have two supplies to the heater - one switched for E7, the other ‘always on’. There has to be power to the heater all the time for both the controls and for the fan that blows warm air out when you need it. This also makes it possible to ‘boost’ the heater’s output, for example if it runs out of steam in the evening when you most need it (any electricity used in this case will be charged at the peak rate). 

So, it should be possible to wire up your new heaters as you want them to be without having to replace the CU. 

I assume your present heaters are switching on and off as you expect them to; some users with newly-installed smart meters found that this wasn’t happening, meaning that OVO’s metering people had to wave a magic wand to get the system working.

A note about E7 tariffs: the way this works with OVO is that all usage in the offpeak period is charged at the cheap rate, while all other usage is charged at the higher rate. That’s why it’s a good idea to run power-hungry beasts like washing machines, tumble driers and dishwashers at night. If you can’t program appliances like this to finish their cycle before 07:00, say, just plug them into timer switches that are off all day and switch on only after the offpeak period has started.