Hammond loudly and Johnson with his consigliere Cummings sotto voce all accept that EU leaders and negotiators do not see ANY way of negotiating a new Brexit deal on the basis of what Britain's new prime minister says he wants.
As one Brussels official confirmed to me, even if EU leaders and especially Ireland's Taoiseach were prepared to do as Johnson asks and rip up the backstop - which they most definitely are not - they could not do so unless Johnson offered a detailed proposal for what would replace the backstop - and he says both that he can't and won't.
"When David Frost [Johnson's Brexit negotiator] came to see us, we asked what would replace the backstop" said an official.
"Frost said that talks on putting in place new arrangements to keep open the border on the island of Ireland would have to take place after the UK leaves the EU, during negotiations on the future relationship between the UK and EU.
"If that happened, we would be abandoning our insurance policy for protecting the single market without having any certainty, any real clue, on what would replace it. That's impossible. We can never do that".
Or to put it another way, the view in Brussels, Paris, Berlin and Dublin is that the locomotive to a no-deal Brexit on October 31 is almost unstoppable, and therefore the priority for them is to put in place measures to mitigate against the most damaging consequences.
These prophylactic measures include probably suspending state-aid rules for Eire to allow the bail-out of businesses hurt by a no-deal Brexit, and making sure individual EU members don't unilaterally agree mini-deals with Johnson that would undermine the EU's unity.
(Some states for example will feel under pressure to protect the rights of their citizens in the UK or make sure their own planes can land in London).
But whatever the economic costs for the EU and especially the Republic of Ireland of a no-deal Brexit, the political costs for Leo Varadkar of being seen to be bullied by a UK prime minister to once again police the border with Northern Ireland (even almost invisible digital and CCTV policing) are simply too great to contemplate.
The point is that Macron, Merkel, Varadkar, Johnson, Cummings and Hammond are all in perfect agreement - that it will be a no-deal Brexit on October 31, unless there is an external or exogenous shock.
Where they differ is that Hammond is desperate to be the midwife of that shock, Macron, Merkel and Varadkar would probably respond sympathetically to it, and Johnson/Cummings would do all they could to repel it.
The shock that Hammond - and other former Tory Cabinet minsters such as Stewart and Gauke are keen to unleash - is the one I've been spouting on about here for some weeks.
Not a general election, which of course is still highly likely, but a revolt by backbench MPs to seize control of the Commons order paper and then pass legislation to make a no-deal Brexit illegal unless first ratified by MPs.
As I've said, this is more-or-less what happened a few days before the first Brexit deadline of March 29.
And there is no reason in principle why it could not happen again in the first two weeks of September - especially since the speaker John Bercow has explicitly confirmed he is minded to facilitate Parliament exercising its sovereignty in this way.
Apart from anything else, when Parliament legislated in March to compel Theresa May to sue the EU for a Brexit delay, her Attorney General Geoffrey Cox told her the law is the law and she must comply.
Johnson kept Cox as his attorney general, a decision he may soon regret.
In case you were in any doubt about the gravity of all this, Hammond and his co-conspirators have already drafted their planned legislation, to force a Brexit postponement, and reassert MPs' right to veto a no-deal Brexit - if that is what they want.
Which means, as if you didn't already know, that the the titanic battle between legislature and executive - between MPs and prime minister - will begin in early September, to determine which of them has best claim to represent the will of the people on how, when and whether the UK leaves the EU.
For what it's worth, my view remains the same, that all this will not and cannot be settled without resort to another popular vote, in a general election.
Johnson would be broken as PM, any hope of governing on anything in a serious way would be lost, if he became Hammond's puppet - he could never recover his authority.
So if it becomes clear beyond reasonable doubt that Parliament both can and will outlaw his no-deal Brexit, Johnson would have no alternative but to try and engineer a general election.
Which is why within Johnson's government there are only two serious priorities, preparations to leave the EU without a deal on October 31 and preparations for a general election around the same time.
Johnson and Cummings would prefer polling day itself to be after the UK has left the EU (1 or 5 November) - because it would be so much easier to defeat an opposition campaigning to rejoin the EU rather than maintain the status quo.
(Just think about the fun Johnson would have pointing out that if the UK wanted to rejoin the EU we'd lose our budget rebate and would be compelled to join the Euro).
But there would be riots in the streets and in the Commons chamber if the election were not a level-playing contest on whether to leave the EU without a deal or remain, so I think such is highly unlikely.
One final thought on why Johnson needs a general election to determine Brexit.
Frost also told his EU interlocutors that Johnson's vision of a future relationship with the EU is a very basic Canada-style free trade agreement, with only minimal harmonisation of rules and regulations.
Johnson knows the overwhelming majority of MPs in Parliament as currently constituted want the UK to be much more intimately linked with the EU in a commercial sense than what he is prepared to accept.
On Brexit, and actually on pretty much everything else, Johnson will be prime minister in name only, without a general election.
For example, Priti Patel has no chance of securing a Commons majority for her tougher law-and-order measures.
So to govern in any meaningful way, Johnson has to take the risk - just a few weeks from now - of giving the British people the opportunity to turf him out.