In a tweet the MoneySavingExpert founder wrote: "Dear @trussliz / @RishiSunak the cost of living crisis has left millions worried how they'll make ends meet.
"I'd like to formally invite you, as the new PM, to join me asap once you take office for a special hour's @itvMLshow discussion/Q&A to answer/ease people's concerns."
Responding to Mr Lewis' social media post, the 75-year-old from Liverpool wrote: "I would like you, Martin, to stop using words like 'catastrophe,' and instead advise people take sensible steps to reduce the effect on their families and businesses.
"And stop pretending that governments can do everything. They can’t."
Money Saving Expert's Martin Lewis during a joint press conference with Facebook at the Facebook headquarters in London.
Kirsty O'Connor
The sharp-tongued riposte from the former minister, who has appeared on several reality TV shows since leaving Westminster, drew fierce reaction from thousands of Twitter users, including Mr Lewis himself.
He shot back: "It is a catastrophe Edwina!
"While there are steps people can take to help themselves... Energy bills by Jan will cost on avg over half the full state pension & bigger proportion of basic UC. No sensible steps cover that!"
TV psych therapist Emma Kenny chimed in to the debate, replying to the ex-politician saying: "Well they could have avoided authoritarian lockdowns, measures including furlough costing billions, shutting down the economy and that’s just for starters!"
Speaking at the final leadership hustings last night, Mr Sunak said “we shouldn’t rule anything out” on energy rationing, with the price cap due to the rise again this winter.
Rishi Sunak and Liz Truss during a hustings event at Wembley Arena, London, as part of their campaign to be leader of the Conservative Party and the next prime minister.
Stefan Rousseau
He also sought to paint himself as the candidate offering a more realistic assessment about the way to approach the economy, with tax cuts not expected immediately if he becomes leader.
Mr Sunak said leadership “starts by being straight with the country about the economic challenges”, adding: “I’ve not chosen to say the things that people may want to hear, I’ve said the things I believe our country needs to hear.
“Although it hasn’t made my life easy, it is honest and, for me, that is what leadership is all about.”
He went on: “My plan is the right plan to tackle inflation, to compassionately support those who most need our help and to safeguard our children’s economic inheritance.
“Because as Margaret Thatcher and Nigel Lawson knew, maxing out the country’s credit card is not right, it’s not responsible and it is certainly not Conservative.”
Liz Truss has claimed there would be no new taxes or energy rationing if she became prime minister, as she dropped further hints about cost-of-living support this winter.
The Foreign Secretary, writing for The Sun, said she is “ready to put my money where my mouth is by cutting taxes” and said her reforms would help “stave off the horror of a recession”.
She added: “I will also deliver immediate support to ensure people are not facing unaffordable fuel bills. I will be robust in my approach. But it isn’t right to announce my entire plan before I have even won the leadership and got my feet under the table.”
Regulator Ofgem has confirmed an 80 percent rise in the energy price cap, which will mean the average household’s yearly bill will go from £1,971 to £3,549 from October.