Just to throw my 2ps worth in:
There's nothing 'wrong' with MI cable as such and it's certainly not 'obsolete', although it's used much less frequently nowadays. The main reasons for this is that it's expensive and can be time consuming to install unless the electrician is used to using it. The reason it wouldn't be OK is the mineral powder used for insulation needs to be kept dry. As already mentioned if the ends were made off properly it should still be fine, but the electrician will do an insulation resistance test to measure just how 'fine' it still is.
I would be more concerned about the layout of the wiring - by the sound of it you're going to need more sockets which will involve new wiring, and the layout could well need changing. Also it could be that all the sockets are on the same circuit, likewise all the lighting. Under the current regulations rcd protection is generally required for all circuits in a way as to prevent disruption, which usually involves 2 rcds in the consumer unit with a lighting circuit and power circuit on each, split across the board so for example if one lighting circuit trips you still have the sockets working in that room so can use a table lamp, light from the tv etc.
This alteration of the layout may mean that although the existing cable might be fine, keeping it could just seem like an exercise in conservation and replacing the whole lot might work out easier and cheaper.
I don't see why you couldn't have night storage heaters, but you'd usually need a separate consumer unit and feed from the meter for them. It's worth considering your energy usage - the whole point of storage heaters is they use cheaper off peak electricity, but on an economy 7 tariff you pay a lot more for electricity during the day, so a modern
electric radiator might work out cheaper for you.
