The former foreign secretary tweeted late last night after the launch of the group’s manifesto at Westminster: “Agree with all of this. One Nation values have never been more important.”
Ms Rudd, the Work and Pensions Secretary, rewarded his tweet with a “like”, signalling she would not rule out the former Mayor of London as a potential leader if he upholds centre-ground values.
An ally of Ms Rudd said: “We want candidates to work with One Nation Caucus to shape policies moving forward, not just on Brexit but on everything. And it’s never been about the person but the policies. We’ve always said that.”
Mr Johnson’s backing for a hard Brexit and courting of Eurosceptics led by Right-winger Jacob Rees-Mogg has overshadowed his more centrist record at City Hall, where he championed immigration and a London living wage.
But a close friend told the Evening Standard: “Boris is, and always has been One Nation. He believes those values — along with getting Brexit right — are essential to beat Jeremy Corbyn and Nigel Farage, whenever the next election comes.”
Mr Johnson had a boost this morning when a straw poll by the Labour List website said he was the potential Tory leader most feared by Labour activists and candidates.
Some 45 per cent said he was the Conservative that Jeremy Corbyn would find most difficult to beat.
All the other names got less than eight per cent with Rory Stewart, Amber Rudd and Michael Gove coming first among the also-rans.
But The Sun newspaper reported that 100 Conservative MPs have formed an Anyone But Boris group to try to stop Mr Johnson from getting into the final ballot of party members in a leadership contest.
Commons Leader Andrea Leadsom said she was “actively considering and preparing” for standing for the leadership this morning.
She indicated on LBC radio that she was just waiting for Theresa May to resign.
“When the Prime Minister decides she is standing down then I will make an announcement,” said Ms Leadsom.
“I don’t want to be a distraction — the PM is working very hard to get Brexit over the line.”
Health Secretary Matt Hancock, the dark horse in the contest, took a packet of caramel waffles to Cabinet to share with his colleagues this morning, capitalising on the publicity he got when caught eating the calorie-laden treat in the street yesterday.
In other leadership manoeuvres, former Brexit secretary Dominic Raab said the basic rate of income tax could be slashed by 5p to “give working Britain a fairer deal” and a typical tax cut of £854.
Treasury Chief Secretary Liz Truss, who is also standing on the Right, said Britain’s 45p top rate of tax was too high and called for “enthusiastic” tax cutting and deregulation, and praised Donald Trump’s agenda.
Mr Hancock told a Telegraph hustings that tax cuts should be accompanied by rises in the National Living Wage to ensure the whole country felt better off from working hard.
Former Cabinet minister Esther McVey claimed some of her Tory colleagues were seeking to “dismantle” Brexit as she launched a new group for “blue collar” Conservatives, seen as a vehicle for her ambitions.
“If that is what the Cabinet is doing, then shame on them,” she said.
Digital minister Margot James suggested any candidate advocating a no-deal Brexit, however, would fail to get backing from the party’s centre.
Home Secretary Sajid Javid said “there won’t be a shortage of candidates” for the job but “whether I will be one of those, you’ll just have to wait and see”.
Mrs May has signalled to Tory MPs she will set out the timetable for her departure and the leadership contest to succeed her after a crunch vote on the legislation for her Brexit deal.
Defeat for the Withdrawal Agreement Bill, which is due in the Commons in the week beginning June 3, would hasten her exit.
Around 25 Tory MPs attended a meeting in Westminster which outlined the One Nation group’s ideas including rejecting “narrow nationalism”, supporting a “strong society” and backing public services.