Energy secretary Amber Rudd will warn Britain's exit from the European Union could result in what she termed a "massive electric shock".
She will say a "no" vote in the in/out referendum on 23 June could lead to "a massive electric shock because UK energy costs are likely to sky rocket by at least half a billion pounds a year — the equivalent of British bills going up by around £1.5m each and every day."
A £500m or more rise in energy bills works out to an additional £20 per household, however this would be about a third less once business consumption is factored in.
Opponents said Rudd's claims show a failure to grasp how energy markets work.
"Far from producing cheap electricity, the EU has done the opposite with some of the highest costs worldwide, relying on expensive renewables," UKIP Energy Spokesman and MEP for the East Midlands Roger Helmer, said.
"Amber Rudd's 'Alice In Wonderland' policies seems to indicate expensive means cheap and cheap means expensive!".
Rudd will also argue that the UK's membership of the bloc helps secure its energy supply from any possible threat by Vladimir Putin's Russia to restrict gas flows.
But during an interview of BBC Radio 4, Rudd was forced to admit that Russia currently provides a very small slice of the UK's energy.
"Very little of our gas we import from Russia at the moment, but what the report says and what I agree with is that in the long term, gas from Russia will play an important part in security in Europe and access to the European market through the internal energy market is how we keep prices down."
"We cannot ignore the role of Russia."