He has what they see as "unique" rapport with that modern breed of "strong man", semi-autocratic world leaders, such as Turkey's Erdogan, Saudi Arabia's MBS and the UAE's MBZ.
"Johnson has a connection with them I've never seen before" said a source. "It is remarkable".
Another said that the UK will therefore lose something important in respect of its international clout when Johnson goes, because "we may not laud or admire these leaders, but we need alliances with them, especially in the struggle to contain Putin".
And then there is of course Johnson's striking emotional connection with Ukraine's president Zelenskyy, which is unrealistic to expect a Sunak, Truss or Mordaunt to precisely emulate.
It seems to be taken for granted that Britain's next prime minister will simply copy and extend the approach of Boris Johnson, namely that Ukraine must be supported economically and militarily in every way short of Britain being drawn into direct conflict with Russia, and that "Putin must fail".
But this is to ignore that quite soon, probably just a couple of months away, western leaders are likely to face a momentous decision - if, as expected by western intelligence sources, Putin requests a ceasefire before the ravages of a cold dark Ukraine winter set in.
All the indications from Kyiv are that President Zelenskyy will reject such overtures from Putin and will see this as an opportunity to deploy new modern western weaponry to displace and demoralise Russian troops, after Russia's grinding recent advance in much of eastern Ukraine.
But Zelenskyy can't be completely confident of western backing. Some leaders are increasingly fearful of the economic and other costs of the war, the dramatic ratchet upwards of oil and gas prices and the tragic shortage of wheat and other basic foodstuffs that is causing starvation in much of the poor world.
These western leaders also note China's determination that Putin and Russia must not collapse, and how China has successfully created a narrative across the developing world, where it has considerable clout, that NATO and the West are to blame for the conflict.
This is why British diplomatic sources are fearful that if Putin asks for a ceasefire, Germany, Italy and maybe other important governments may ask Zelenskyy to consider it, as the possible basis for peace talks.
The point is that if Zelenskyy said no to a ceasefire, it's pretty clear he would be backed by Johnson. But Johnson will presumably by then be pre-occupied by finding gainful employment to service his debts, so the decision would fall to a Sunak, or a Truss or a Mordaunt.
Presumably they'll all stick with Zelenskyy. But we can't know that for sure. Just as we don't really have a sense of how they will approach what some would define as the more important long-term question, namely how to manage diplomatic and trade relations with a China that has taken Putin's side.
The consequences of mucking this up are significantly greater than the timing of cuts to personal taxes, though you wouldn't perhaps get a sense of it from all the noise and heat of the potential PMs' so-called debates.
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