Economic policy, said Nigel Lawson, can only be a success if “there is, and is seen to be, full agreement between the prime minister and the chancellor.”

The fact that he wrote those words in his 1989 resignation letter to Margaret Thatcher is testament to just how difficult – and, indeed, rare – it is for the two most powerful ministers in the country to live in harmony.

Boris Johnson already knew it, having lost Sajid Javid as chancellor last year in a power struggle over staffing arrangements. But he now faces the potentially far more damaging prospect of a fall-out with Javid’s younger and equally ambitious replacement, Rishi Sunak.

Until now, Covid had left little room for bust-ups between Nos 10 and 11 – with the country facing economic disaster, Sunak had no choice but to turn on the spending taps to keep jobs and businesses afloat.

The battle against coronavirus appears to be largely won, however, meaning normal service is already being resumed in the age-old tug of war over the national purse strings that has, more often than not, ended in acrimony.

At best, most prime ministers have come to view chancellors as men (we are still waiting for our first female chancellor) who stand in the way of their grand plans, whether it be for spending, tax cuts or reform. At worst, their next door neighbour is after their job.

Whichever way you look at it, Rishi means business

Rishi Sunak undoubtedly wants to succeed Boris Johnson as prime minister, using his ‘Rishi’ signature to brand big economic announcements, in the hope that the public will view him as PM-in-waiting.

However, of the 34 chancellors to hold the office in the past 100 years, only seven have gone on to become prime minister; many of the other 27 were returned to backbench obscurity by PMs who lost patience with them.

History tells us that few prime ministers are happy to anoint a chancellor as their heir (more often viewing them as a rival), and that even those who do can never guarantee a succession. Just ask George Osborne.

Lord O’Donnell, who, as cabinet secretary, worked for three prime ministers, knows better than most why the relationship between PM and chancellor is so difficult. He says: “A certain amount of creative tension is healthy, because if the prime minister and the chancellor get on too well, things can go badly wrong.

“There is always a temptation for prime ministers to go soft on spending, particularly on defence and foreign policy, and you need a strong chancellor, who doesn’t necessarily get on with them all the time, to convince them all these things need to be paid for.”

O’Donnell says that while Tony Blair and Gordon Brown had a famously tempestuous relationship, in which Brown was both heir and rival, it was nevertheless a success, as they made the Bank of England independent, introduced three-year spending reviews and kept Britain out of the euro.

And while David Cameron and George Osborne had the friendliest working relationship of recent times, “you could argue that if Osborne had been tougher on the Brexit referendum, he might have saved David a lot of hassle,” says O’Donnell.

Cameron and Osborne grew up together on the backbenches and, unlike Thatcher and Lawson (or Thatcher and Howe), shared the same worldview when it came to economic policy.

They were unique in recent times as a chancellor and prime minister who worked hand in glove, with a clear understanding that Osborne was Cameron’s natural successor, though their plans were, like so many, undone by events.

“It was purely down to their personalities,” said one former minister who worked under them. “They were both incredibly laid-back, both from similar, wealthy, backgrounds, they were great friends before they entered government, and Cameron trusted Osborne and relied on him hugely to help him run the country. Blair, on the other hand, didn’t trust Brown or Brown’s instincts, but Brown was so powerful, he couldn’t be sacked.”

Johnson and Sunak do not have the same shared back story as Cameron and Osborne; the two men are not even from the same generation, and even the most civil of relationships will be tested by a system geared up to pit PM and ‘CX’ against each other.

One former adviser to Theresa May said: “When I started at No 10, I was taken aback by that tension between the prime minister and the chancellor. The chancellor’s political fortunes are judged on the fiscal probity of his conduct, whereas the PM is judged on the day to day benefits of spending public money.

“The Treasury is filled with civil servants and advisers whose job it is to tell the chancellor to say no to things. They will be constantly telling the chancellor not to set a precedent by giving in to things – that if they agree to one thing, they will be expected to agree to another, and another.”

The former adviser said May and Hammond were “constantly squabbling over small amounts of money”, and recalled an occasion when May needed to find money to scrap child burial fees in the wake of a popular newspaper campaign. “May won in the end, but Hammond really dug his heels in over what was a ridiculously tiny amount of money, but which had huge political impact,” the source said.

A similar problem reared its head last year when the Government tried to resist calls from the footballer Marcus Rashford to pay for free meals during school holidays, only to cave in, and commit to extra spending, when its position became politically untenable.

The problem, as both Sunak and Johnson know all too well, is that voters and Tory backbenchers simultaneously want two things that are incompatible with each other.

“Backbenchers and the public want fiscal prudence, but they also want governments to spend money on things they regard as important,” said the same source.

“Politics is incredibly easy if your job is just to agree to spending money. Anyone can do that. The real skill is managing the public finances and deciding what not to spend money on. That is true times 10 in the current situation, with the Covid bill to pay.”

Tony Blair and Gordon Brown had a famously tempestuous relationship, but it was nevertheless a success

Credit: PA

For Sunak, the priority is getting the economy back on an even keel and holding up the Tories’ hard-won reputation for fiscal responsibility. Johnson wants to keep on spending, by fixing social care with a ‘Marshall plan’ for green growth, and by launching a new Royal Yacht Britannia, among many other things – though he does not want to increase taxes to do it.

Many wise old heads believe the really dangerous waters, however, will come if Johnson and Sunak decide to break manifesto pledges, as voters tend to be unforgiving when prime ministers renege on promises on which they were elected, such as keeping the pensions triple lock, which Sunak believes can be ditched, if only temporarily.

One former Treasury minister said: “When people become Chancellor, they suddenly realise how much power they have, because they really can stop the Prime Minister’s pet projects if they want to.

“But you can take it too far, and if you rein in the Prime Minister’s plans without showing due respect, you will be sacked.”

No one in the Government believes Rishi Sunak is anything other than secure in his job, but nor is he the master of his own fate.

While Johnson might regard Sunak as the best man to take the wheel once he is ready to move on (which few prime ministers ever are), his patience might run out if Sunak continues in his overt attempts to outshine the PM in the court of public opinion.

And if ideological differences open up between the two men, Sunak could find himself out of No 11, like Howe, who fell out with Thatcher in 1981 after telling her she could not “make water flow uphill”; Lawson, who opposed the Poll Tax and quit in 1989 over Thatcher’s preference for her economic adviser, Sir Alan Walters; and Norman Lamont, who believed Sir John Major had used him as a human shield against his Exchange Rate Mechanism policy failures.

Sunak will also be well aware that his own popularity, cresting a wave of money for furlough and business grants, may soon take a downturn once taxpayers’ cash has to start flowing the other way.

In that event, he will need Boris Johnson’s support and patronage more than ever – particularly in Cabinet, where cash-hungry secretaries of state might tire of him saying no.