Mr Wright said that because Britain has lost fuel capacity because of the closure of coal mines, there is now “much less flexibility” for suppliers.
In a stark warning about the future of energy supply in Britain, Mr Wright said that consumers could be forced to pay more if they want to ensure they always have power.
“At the moment everyone has the same network – with some difference between rural and urban – but this is changing and these changes will produce some choices for society,” he told a recent conference.
“We are currently all paying broadly the same price but we could be moving away from that and there will be some new features in the market which may see some choose to pay for a higher level of reliability.
“One household may be sitting with their lights on, charging their Tesla electric car, while someone else will be sitting in the dark."
Mr Wright, who Ofgem last night insisted was speaking in a “personal capacity” appeared to lay blame to any future supply issues on the recent focus on renewable energy.
He said: “The system we are all familiar with has some redundancy built into it. It was pretty straightforward and there was a supply margin, but increasing intermittency from renewable energy is producing profound changes to this system.
“We now have much less flexibility with the loss of fossil fuel capacity. Coal has been important, but this is disappearing.”
He added: “In the future not everyone will be able to use as much as electricity as they want, and there will be a need to re-write the rules.”
An Ofgem spokesman said: " Ofgem is fully committed to delivering secure supplies for all consumers now and in the future. This is our number one priority. This is why we have driven up network reliability standards and worked closely with Government to ensure secure energy supplies."
“In order to protect consumers every regulator has to look a possible future challenges. Mr Wright was talking at an University conference in a personal capacity and looking at possible issues that might or might not arise in 10-15 years time.”
Philip Hammond, the Chancellor, has previously said that Britain will need to invest "eye-wateringly large sums of money" just to keep the lights on.
The Chancellor put the cost at around £100 billion in the next 20 years to ensure the country meets its energy needs.