Mr Rees-Mogg, whose full-blooded Toryism and unabashed poshness has led to him being nicknamed “the Honourable Member for the 18th Century”, has consistently backed Ms May as party leader in public.
But on Sunday – against a background of increasingly enthusiastic “Moggmentum” social media campaigns by youthful Conservatives – two separate newspaper reports said he was “sounding out” friends about a possible leadership bid, and would like to succeed Ms May “when the time comes”.
The Sunday Times reported that ‘friends’ said the pro-Brexit Old Etonian was “sounding out” trusted confidants and giving “careful consideration” to his political career – despite also carrying an interview in which Mr Rees-Mogg said: “I’m supporting Theresa May … If I threw my hat into the ring, my hat would be thrown back at me pretty quickly”.
The Mail on Sunday quoted the Anglo-US academic Ted Malloch – who has close links to Donald Trump – as saying: “I was at a lunch with Jacob very recently and he indicated he would like to be considered for the leadership when the time comes.
“He did not mean now, but at some point in the future.”
Mr Rees-Mogg confirmed having lunch with Professor Malloch, but denied saying he wanted to be Tory leader.
If, however, Mr Rees-Mogg were to become party leader – and Prime Minister if the contest happened while the Conservatives were in power – it would be in the teeth of bitter opposition from some of his fellow Tories.
“His manners are perfumed but his opinions are poison. Rees-Mogg is quite simply an unfailing, unbending, unrelenting reactionary.
“His record on every moral, social, sexual or reproductive issue I’ve looked at is brute moral conservative. He has been a straight-down-the-line supporter of every welfare cut I’ve checked.
“Examining his stances and his reasoning one sees the intellectual nimbleness of a top QC and the opinions of a Colonel Blimp. On Europe, his instincts would take Britain crashing out with no deal at all.”
While not going as far back as the 18th Century, even Mr Rees-Mogg’s most admiring parliamentary sketchwriters have called him “the Honourable Member for the Early 20th Century”.
With his fondness for three-piece suits and carefully modulated Edwardian vowels, he has never attempted to disguise his privileged upbringing – although he has consistently denied reports that while campaigning in the safe Labour seat of Central Fife in 1997, he toured the constituency with his nanny, in a Bentley.
He insists it was a Mercedes.
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Living in a Grade II-listed manor house, while consistently voting against the so-called ‘mansion tax’, Mr Rees-Mogg married the heiress daughter of the Marchioness of Bristol after reportedly proposing to her beneath one of the six Van Dycks that adorn her family’s stately home in Kent.
He later described himself as a man of the people, in Latin.
While risking class envy among some voters, such quips have led to Mr Rees-Mogg being idolised by his right-wing, pro-Brexit fans as the refreshingly “authentic” man to “lead the Conservative fightback”.
Ready for Rees-Mogg, an online petition calling for him to run for Tory leader started by two former Vote Leave campaigners – Anne Sutherland, a Scottish Conservative, and Sam Frost, a digital strategist who worked for Ukip in 2015 – has now attracted more than 22,000 signatures.
Facebook pages including Moggmentum, the Jacob Rees-Mogg Appreciation Society and Can’t Clogg the Mogg have attracted about 40,000 ‘likes’.
Although the numbers remain far behind the 165,590 likes and 78,000 twitter followers of the left-wing Corbynista Momentum movement, the hope seems to be that Mr Rees-Mogg could become the ‘Tory Corbyn’: initially ridiculed by the party establishment, but coming from the backbenches to win the leadership thanks to the support of grassroots activists.
Last Wednesday a survey of Tory party members by the Conservative Home website showed that Mr Rees-Mogg was now their second most popular choice to succeed Ms May as leader, after Brexit Secretary David Davis.
If Mr Rees-Mogg did become leader, one possible insight into what he might want to do as Prime Minister was provided by a speech he gave to the Centre for Policy Studies think tank in May 2012.
“It is time,” he declared, “For full-blooded Toryism with confidence in our country and courage in our convictions and a smaller state.”
Mr Rees-Mogg’s voting record might also suggest how the MP for North East Somerset would achieve “a smaller state”.
While opposing a ‘mansion tax’ on homes over £2m – proposed by Vince Cable as a means to fund a tax cut for those on middle and low incomes – he has voted 16 times in favour of reducing housing benefit to social tenants deemed to have an excess of bedrooms. (The so-called ‘bedroom tax’.)
The son of Lord Rees-Mogg, a former editor of The Times, he has also consistently voted against raising benefit payments in line with inflation.
Between 2011 and 2016, according to the TheyWorkForYou website, Mr Rees-Mogg voted 14 times against measures that would have given higher benefits over longer periods for those unable to work due to illness or disability.
In February 2012, for example, he voted against allowing cancer patients to be excused from the 365-day limit on receiving contributions-based Employment and Support Allowance.
He voted to repeal the Human Rights Act in December 2012 and May 2016, and as a Catholic father-of-six he has consistently opposed gay marriage. In 2013 he said that on same sex partnerships, “I take my whip from the hierarchy of the Roman Catholic Church rather than the [Conservative] Whip’s Office.”
Mr Rees-Mogg has also supported zero hours contracts as convenient for employers and for employees, especially those seeking to get their first job.
Denying such contracts were exploitative, he wrote in the Telegraph in August 2013: “The promise of welfare and welfare regulation mean that there is no incentive to accept jobs that do not meet basic standards.
“The model of the flint-faced Victorian employer grinding the poor never was particularly accurate but today such an image is even more false.”
His May 2012 Centre for Policy Studies speech also contained passages where he questioned the wisdom of the UK’s current overseas aid budget and anti-global warming targets.
Insisting that it was “necessary to re-visit what the state provides and where the spending goes”, he urged cutting the overseas aid budget because “This is not the job of government but ought to be a matter of private charity.”
Hinting that he wanted to do away with some anti-global warming targets, he added: “Environmental and recycling targets need to be looked at to see if they serve any useful economic purpose or are merely part of green orthodoxy.
“Even if the greens are right, Britain will make very little difference on her own and I would rather my constituents were warm and prosperous rather than cold and impoverished as we are overtaken by emerging markets who understandably put people before polar bears.”
Mr Rees-Mogg has also issued statements in support of Donald Trump, telling the BBC days after the election of the US President in November 2016 that the victory was “good for the US [because] he is looking to cut taxes and deregulate”.
Mr Rees-Mogg added: “I think for Britain, it [Trump’s election] is much better than a continuation of the Democrats. We have so many shared values and a commonality between Brexit and the election of Trump is that it is the triumph of optimism.
“This is a wonderfully optimistic, outward-looking approach and has great opportunities for both our nations to work together and collaborate to the good of the world.”
His fellow studio guest, the ex-Labour leader Ed Miliband, immediately responded by saying: “What we just heard was delusional fantasy. The idea that we have shared values with a racist, misogynistic, self-confessed groper beggars belief.”
At the time of writing, the Ready for Rees-Mogg petition has 22,324 signatories.