These are UK wholesale prices (i.e. the price electricity is sold by producers for delivery on the high voltage grid), which are expected to jump massively this winter in the steps of gas prices.

As you implied, retail prices are the addition of wholesale prices, distribution costs and taxes. In a number of countries they are still regulated closely by the State or public authorities (for instance by public bodies in each individual State in the US).

When wholesale prices increase like this, producers request to pass this on to consumers, and it eventually happens, so Britons should expect significant increases in coming months.

The reason why gas prices determine power prices even though gas power plants only make 30% or so of the production capacity in the UK is simple: they are the marginal plants. By this, I mean that when power demand goes up or down, it is gas fired plants that are turned on or off, because (i) it's the most expensive power source and (ii) it's the easiest to turn on and off. Coal and nuclear are cheaper (and nuclear is hard to stop anyway). Wind is way cheaper when it produces. so these are pretty much always on, thus leaving the adjustment to the gas side. The production cost of the plant turned on or off becomes the price for the whole market. If gas prices go up, so will the clearing price for power.

This is happening on a violent scale in the USD today.

So back to Dodo's point: competition makes producers more efficient, maybe, but it makes prices more volatile. It has also encouraged investment quasi excusively in gas fired plants at the exclusion of everything else because they are the only plants for which you can get a return on less than 10 years (coal and nuclear are cheap also in part because they can be amortised over 40 years or even more) and are thus the only kind to attract private investment.

This has brought the boom and bust typical of many sectors, except that with a product that cannot be stored, it brings about much more brutal price spikes when supply is unsufficient. and it has had unexpected consequences on the gas market which, to put it simply, has not been able to cope with that sudden surge in demand. Thus higher prices, a "normal" market phenomenon which pro-liberalisation politicians seem somewhat embarrassed to acknowledge...

In the long run, we're all dead. John Maynard Keynes

For that matter, learn from the 19th century.  

Deregulation of natural monopolies is a scam.  

Replacement of regulated monopolies by unregulated oligopolies is also a scam.  

The US has been looting its own economic and social infrastructure for 25 years now.  It is now far to late to avoid a complete crash.  What about Europe?  Are you stuck on the same road or do you have a window of escape?  

The Fates are kind.