I would expect it to be OK if the customer does not demand the most powerful shower and induction hob.  Diversity is wonderful in most domestic situations.. Unless they are cooking three course lunches while someone takes long showers it is unlikely there will be an overload.I would recommend an off peak immersion with a boost function from the normal supply. I would also question if they have hot water from the immersion why they need an electric shower as well. If the storage heaters are properly sized there should be little additional heating load, they have improved considerably compared with the old ones that usually ran out of steam in the late afternoon just when most people wanted heating. But at the end of the day you are the one who knows the customer, their lifestyle and the size/condition/insulation/ventilation  of the flat. 

As Mike has said there are also load shedding/priority relays available and there was a recent thread about diversity regarding a situation similar to your's.

I would expect it to be OK if the customer does not demand the most powerful shower and induction hob.  Diversity is wonderful in most domestic situations.. Unless they are cooking three course lunches while someone takes long showers it is unlikely there will be an overload.I would recommend an off peak immersion with a boost function from the normal supply. I would also question if they have hot water from the immersion why they need an electric shower as well. If the storage heaters are properly sized there should be little additional heating load, they have improved considerably compared with the old ones that usually ran out of steam in the late afternoon just when most people wanted heating. But at the end of the day you are the one who knows the customer, their lifestyle and the size/condition/insulation/ventilation  of the flat. 

As Mike has said there are also load shedding/priority relays available and there was a recent thread about diversity regarding a situation similar to your's.