First I'd like to take to task all those that wish to remove the so-called perverse pricing incentives for increased consumption.  We have cheaper electricity at certain times of the day and night to allow us to economically run off peak heating systems in the winter and air con during the summer.  This is simply demand led pricing, we get cheaper power off peak because the power companies are trying to stimulate demand (or push some of the variable demand to off peak times eg washing machines/tumble driers).
In our situation we certainly don't get cheaper power if magically double our consumption.  The cost benefits are there to incentivise us to help balance the load on the grid and allow us to heat our home affordably.  Even at 4.5p/kWh the power co are still making money.  
The suggestion of allowing each house cheap power up to a certain value for heating/cooking lighting and then increased power thereafter has merit, but who gets to decide what a reasonable level is.  It would vary massively for different values of insulation/efficiency.  Lets not forget that here in the UK we're cursed with a huge amount of 100+ year old housing stock, which isn't about to disappear anytime soon.  Laughably much of our very recent housing stock is just as inefficient as the stuff built just pre and post WW2.   I should know, my house is but 20 years old and is draughtier and less well insulated than my parents 1930's semi detached.  Where I live it seems modern housing is built down to a price, not up to a standard.

So how do you decide what is required for a given house for its base load heating/cooking.  What about size?  Would you get a bigger allowance for more sq meters?  You'd certainly need it for a large family home vs. a small starter flat.

The whole scheme is just ripe for political interference, with extra "base" allowance being granted if you're "poor", on benefits, an asylum seeker, labour voter etc etc.  Soon those who can be squeezed for extra cash will end up subsidizing those voted in a certain way.  Don't think this will happen?  It already is with council tax.  More central govt. cash making its way to "favoured" areas, with other areas having to increase council tax to cover costs.  Unsurprisingly favoured areas happen to be mainly Labour controlled.  I would not be surprised in the slightest if the opposite happened under a Conservative govt.  Both sides are as bad as each other.

No, if anything the energy markets should remain free of this kind of political interference.  Price should be set by the open market.  The Govt. role should be limited to long term strategic policy making to encourage efficiency and encourage new gen. capacity to be built in a way which will not leave the UK venerable either economically or socially.  We will not be able to compete with other economies in the next 30 to 50 years if we make the wrong decisions now.  Further power outages will make UK plc a very unattractive place for business if allowed to occur, so to say that we will have to curb demand is slightly naive.  Sure, efficiency can help, but to expect industry to simply switch off to help reduce carbon emissions/reduce fuel consumption is not going to happen.  Industry will simply relocate elsewhere.

If we're not careful that elsewhere will be France, with its nice stable nuclear capacity.