I can't comment on palaces, but certainly the use of electricity spread quite slowly in Britain. My father tells me that his parents' house (in a middle-class part of Liverpool) didn't have electricity until the 1950s. Early in 1947 bad weather resulted in problems getting coal to power stations, and various coastal towns received assistance from the Royal Navy. Non-nuclear submarines use their diesel engines to charge up the electric batteries they use under water. Apparently, connecting up one or two submarines to the town electricity supply was enough to deal with any shortfall from the power stations. Quite apart from the ingenuity involved, it does suggest that demand for electricity was quite low compared with that of today.
However, it doesn't surprise me that Nicholas got an electric generator for the Alexander Palace.
Ann