I'll add a bit of balance to this.
The energy companies don't make a particularly great profit margin - certain companies produce bills which actually show how little profit they have made from their customer in the billing period.
Typically profit margins are only mid-single-digit percentages; food retailers about the same margins.
The water companies who nobody seems to notice, get away with about three times that profit margin, as do the big telecoms companies such as Vodafone and again the same profit margin for the manufacturers of branded goods off supermarket shelves (i.e. Unilever make about 15% profit margin, with ASDA making their 5% margin on top of that).
Note also that customers are free to switch utility providers. The electricity market has competition and there are regulators.
However, let's suppose we nationalise all the utility companies as "not-for-profit" state-owned businesses.
The mid-single-digit percentage profit margin would be about all that could be trimmed from customer's bills. So bills, on average, might be several percent lower. Say from £120 per month to £110 per month.
On the other hand, with all companies being government owned, there would be no profit incentive for companies to be lean, mean and cost efficient nor to invest in new tchnologies.
So I suspect that nationalisation would, eventually, result in much higher bills due to bureacrats and the typical government waste which dogs anyting government-owned, including the likes of the very-inefficient NHS. I worked for the government for a number of years and the inefficiency was shocking, caused largely by lack of competition meaning no need to advance technolocgy and no great pressure on the managers to exceed any targets. In fact, we were lucky if targets were actually met, and it was common for only the target to be met, while everything else was neglected because it wasn't being measured.
So if anyone thinks that utilities would be cheaper if government-owned, I think they'll be dreadfully disappointed. Do you really think that the government can run a business at competitive prices? Many nations have tried communism before; it usually fails.