We hope that patients, doctors, nurses, midwives, paramedics, cleaners, porters, caterers, medical secretaries, clerical staff and all who sail in the good ship NHS are duly grateful to Dominic Cummings this morning.

For it was the polling and focus group work of the former Vote Leave director, interpreted by his political vision, that resulted in a centrepiece of the organisation’s victorious campaign – the idea that the payments which Britain makes to the EU could be turned into £350 million a week for the health service.

Without it, Leave might not have won.  Without it, there would certainly have have been no pressure to honour the commitment (Boris Johnson has hammered away, from time to time, on the point in ministerial meetings.)  So without it, the NHS would not have had gained the £384 million a week extra which, we read, will now come.

The service would doubtless have been chucked some extra dosh to honour its 70th anniversary, but doubtless not quite as much.  Jeremy Hunt links Brexit and this new NHS money together this morning.  “That famous campaign promise can now unite us all,” he writes, “the British public voted for £350 million a week for the NHS, and that – and more – is exactly what this Government will deliver”.

Remainers and Leavers will argue until Brussels freezes over about whether £350 million will fully come back at all, or will partly be spent elsewhere, or will be exceeded by lost tax revenue, or is an accurate figure in the first place.  One point is certain: that when it comes to telling less than the truth, both the official campaigns were “in it together”, as George Osborne once put it.  (Yes, that’s the same George Osborne who claimed that Brexit would bring an immediate recession.)

But at any rate, both quarrelling parties ought to be able to agree that the UK will not stop making payments to the EU at a stroke.  Indeed, some money will still be flowing to it on as distant a date as 2064.  Philip Hammond must find some of the new NHS money from growth, borrowing, tax rises, spending reductions elsewhere, or all four.  How much from each?  We apparently won’t know until the Budget, though there are likely to be stealth tax increases, such as frozen thresholds.

It is at this point that the logic of policy-making by focus group begins to break down.  How would frozen thresholds be compatible with the Conservative Manifesto commitment to “as promised, increase the personal allowance to £12,500 and the higher rate to £50,000” by 2020?  And how does bunging a Brexit dividend plus stealth tax rises at the health service actually work – in either NHS or wider terms?

There are three main issues.  First, the service will reportedly have to ensure that the new spending delivers value for money.  But, with all due respect to Downing Street and the Health Department, this is the same old song.  The cash will most likely vanish into the service’s gaping maw.

Second, public gratitude will be strictly limited, if real at all.  The Health Foundation is already out and about suggesting that the new money will not be enough.  Simon Stevens, the trade unions, the Opposition, the health lobbies – none will simply throw up their arms to heaven in gratitude, and sing the Alleluia chorus.

Finally, the increase raises the alarming possibility of a complete breakdown in Ministerial order.  The Sunday Times claims that the details of the announcment “were finalised at 5.30pm on Friday after Jeremy Hunt, the health secretary, told his closest allies that he was prepared to resign if he did not get the money he was demanding”.

Whatever the full facts may be, the package can only be read as a big win for Hunt, who has increasingly been operating as an open campaigner for more NHS cash, and a consequent defeat for a Chancellor who, despite his successful Budget of last autumn, is unpopular with Brexiteers, kept well away from voters, and is now vulnerable to pressure from his colleagues.

Like sorrows in Hamlet, spending bids come not single spies, but in battalions.  Gavin Williamson wants more money for defence.  Sajid Javid has marked his arrival at the Home Office by suggesting that the police need more, too.  James Brokenshire has local authorities knocking at his door.  Damian Hinds can point to parents up in arms about schools spending during last year’s election.

And now Hunt wants more for social services, too.  We’ve said it before, and say it again: a nation cannot tax its way to prosperityor to a better NHS for that matter.  Nor can it let borrowing take the strain instead: the roof must be fixed while the sun is shining, as someone or other once put it.  Too few Ministers get the point: Javid (overall), Liz Truss, David Gauke, Hammond himself – not many others.

But if it isn’t a happy day for the Chancellor, it most certainly is some of his colleagues.  The news marks a win for Johnson and Michael Gove as well as Hunt.  And it comes nicely in time for this week’s further debates on the EU Withdrawal Bill, a point that will not be lost on the whips in their conversations with potential rebels.

As for Cummings, perhaps a giant gold Turkmenbashi-style statue should be hauled up in his honour in his home city, Durham, to mirror that of Aneurin Bevan in Cardiff. They could frown and wink across Britain at each other, like the Two Towers in The Lord of the Rings.