Energy provider Scottish and Southern Energy and distributor UK Power Network have agreed to pay out a total £8 million over their handling of last year's winter storms.
An additional £3.3 million has been secured by regulator Ofgem after the £4.7 million already paid out to customers over "exceptional" storms last Christmas in the south of England.
Energy regulator Ofgem is to more than double the minimum compensation payment for households that suffer power losses due to severe weather.
Affected customers will now receive at least £70 if they experience an outage of more than 24 hours.
Over three quarters of tenants have never switched electricity provider, according to the latest data from Ofgem's 2014 Consumer Engagement Survey.
The poll revealed one in five tenants did not know they could change energy providers in what the industry regulator dubbed the "sheer lack of awareness" of renters' rights to shop around.
A further 74% admitted to never switching to another gas provider.
Ofgem said that although renters often thought they had to accept the energy suppliers already in place when they moved in, this was very rarely the case.
Chief scientist at Greenpeace UK - Dr Doug Parr - has said the energy industry needs "real change," rather than an investigation by the Competition and Markets Authority.
What UK consumers need from this investigation is more than yet another ineffectual slap on the wrist for the big six's cartel.
We need real change to the market so that companies offering a better deal for customers and the environment are no longer shut out of the market, but more importantly we need to clear the way for alternative business models to the big utilities.
Following Ofgem's announcement that the Competition and Markets Authority will hold a full investigation into the Big Six, ITV News' Business Editor Joel Hills asks why more of us aren't switching from the big six energy suppliers?
Ofgem's investigation into the Big Six energy firms should help "rebuild consumer trust and confidence" in the energy market, the watchdog said.
Ofgem says soaring household bills and intensifying public distrust highlighted the need for an investigation, which will determine whether the companies were making excess profits, after they quadrupled to more than £1 billion in three years.
The Competition and Markets Authority (CMA) probe comes after latest figures show that household electricity by prices in the first three months of 2014 were almost 6% higher than last year.
The investigation, expected to take around 18 months, will look at the relationship between the supply businesses and generation arms of the Big Six energy firms.
Ofgem's investigation into the Big Six energy companies comes after customer complaints relating to energy firms reached the highest number in a single quarter since records began.
The energy suppliers received a total of 1.7 million complaints, with Npower receiving the highest number of 83 complaints for every 1,000 customers.
SSE, British Gas and E.On all received around 30 complaints, with SSE's figures doubling from 13 to 27 on the same time last year, while Scottish Power received the fewest at 13.
"Yet again millions of customers are being let down by poor service from the Big Six energy companies. This has to change," Which? executive director Richard Lloyd said.
Consumer rights group Which? has welcomed the investigation announced by Ofgem into the UK's energy market.
"a watershed moment for the broken energy market and millions of people struggling to cope with spiralling bills" says Which?.
The investigation must leave no stone unturned in establishing the truth behind energy prices - says Which? @whichcampaigns
Ofgem is referring the energy market to the Competition and Markets Authority for a full investigation, it announced today.
The energy regulator Ofgem has written an open letter to the Big Six energy companies asking them to explain to customers why their bills have not fallen despite a drop in wholesale energy prices.
But the firms are saying it is more complicated than it would seem because much more than wholesale pricing goes into making up the cost of our bills.
The government said the companies would do well to listen to the letter or face action - the toughest of which would be a full competition inquiry.