The business reporter is Dearbail Jordan.
Up to 40% of its customers will be in fuel poverty by October, as it called on the government to help struggling homes.
Michael Lewis said the rise in energy prices is unprecedented and a growing number of its customers are in arrears.
There are calls for the government to impose a windfall tax on oil and gas firms.
The Secretary said that Sunak will look at all options.
He told the BBC that they had 22 billion dollars in the next year to help people who need it the most.
Mr Lewis said that around one in eight of its customers were already struggling to pay their bills, even before the weather turns colder and the new energy price cap comes into force in October.
He told the Sunday programme that we need more intervention in October.
A household is considered to be fuel poverty if it spends 10% or more of its disposable income on energy.
Around a fifth of its customers are already in fuel poverty, but that is expected to rise later this year, according to Mr Lewis.
The price cap on gas and electricity was lifted by Ofgem in April.
The price of energy has gone up for 4.5 million people who use pre-payment meters, by an average of over 700 dollars a year.
The price cap is expected to go up due to the rising cost of gas, so the typical energy bill is expected to go up.
Mr Lewis has been in the energy industry for 30 years and has never seen prices increase at this rate.
The UK's inflation rate reached a 40-year high of 9% after gas and electricity prices went up in April.
He wouldn't say if the government should impose a windfall tax on companies that benefit from the rise in crude oil and gas prices.
Mr Lewis said that the government taxes those with the broadest shoulders.
In the first three months of this year, Shell made a record 7 billion dollars in profit, while BP made 5 billion dollars.
The word could be heard four times.
He used it many times and asked the government to help energy customers who were facing huge bills.
The chief executive of a huge energy firm admitted that the scale is too big for them to manage.
Mr Lewis made suggestions on what policy tools the government could use to help his customers, 20% of whom are now in fuel poverty, a figure that is expected to double.
The Treasury is under pressure to find solutions to the cost of living crisis to help people who are struggling. The candour from the top of business will add to that.
Labour, the SNP and Liberal Democrats all support a windfall tax.
Boris Johnson is reluctant to introduce a tax because it could hit energy firms investments in the UK. According to the Sunday Times, the chancellor is considering a levy.
Mr Sunak told the BBC that he was not attracted to the idea of a windfall tax.
These companies are making a lot of money at the moment because of the high prices.
Mr Sunak wants to see significant investment back into the UK economy to support jobs and energy security.
No options are off the table if that doesn't happen.
Mr Lewis thinks that the government could increase the size and scope of the Warm homes discount scheme.
Those in receipt of certain benefits can seek a one-off payment.
The scale of the scheme is too large for us to manage, according to Mr Lewis.
If we were to expand the scope from three million to six million customers and increase the payment from Affirmative to Affirmative, it would make a big difference to those customers on lower incomes.
While we can't shield everyone from the global challenges we face, we are supporting British families to navigate the months ahead with a 22 billion package of support.
The chancellor has made it clear that as the situation changes, our response will evolve and we are ready to do more.
Mr Lewis claimed that energy providers were limited in the help they could give customers because Ofgem set gas and electricity prices.
Jonathan Brearley is the chief executive of Ofgem.
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