There have been faults on both sides of this bargain this week. On the Queen's side, there has been too much reliance on precedent. She was slow to recognise that the formal protocol of flags, for example, should be adapted to the needs of the moment. Many of these alleged traditions have been invented quite recently in order to enhance the monarchy's prestige and should be reinvented ruthlessly to preserve it.
On the people's side, or at least on the people's behalf, some of the insistent demands of the press for a more public show of grief have been quite mawkish. The Queen was quite right to resist the implication that she and her family should have spent the last few days publicly rending their raiments.
However, the Royal Family know that they have been slaves to public opinion ever since Queen Victoria managed to salvage something from the wreckage of Britain's becoming a full-blown parliamentary democracy. George V's invention of the modern monarchy - changing the family's name from Saxe- Coburg-Gotha to Windsor, starting the fashion for glamorous royal marriages (that of the present Queen's parents in 1923) and confecting the concept of the Silver Jubilee in 1935 - was a triumph of public relations.
The terms of the deal were advantageous to both sides, but there was more than a hint of Faust about them. The public and the press were deferential then, but have become imperious. What the people want, the people must have. In order to earn the doubtful privilege of living like royalty, the Windsors must now behave themselves, pay taxes and, this week, indulge in public displays of emotion.
That the monarchy should be more in touch with the lives of its people is right. But that it should be dictated to by the crowd is not. As David Steel said, it was "quite monstrous" to expect the Royal Family to come to London and "put on some sentimental show", and yesterday's attempts to respond to the national mood came close to being precisely that.
The acute dilemma faced by the Royal Family is that in her life Diana embodied the demonstrative approach. Her last public statement concerned her differences with the traditionalists in "The Firm". In Le Monde, five days before her death, she commented on a photograph of herself cradling a dying boy in Pakistan. She had been criticised within the Royal Family, she said, for doing what came naturally to her. "That's why I annoy certain people. Because I'm closer to people below me than to the people above me, and the people above me don't forgive me for it. Because I have a real relationship with the most humble people."
It was her willingness to touch the lost and the hurt which endeared her to so many millions. This must be hard for Charles, who is also concerned about the plight of the underprivileged, although he expresses it in a less demonstrative way, and it would not be convincing if he now started publicly to embrace leprosy or Aids sufferers.
Nor does it follow from Diana's popularity that most people actually want a head of state who declaims, "I feel your pain," as President Clinton did. And it is unclear whether the public genuinely want a Royal Family that is "just like us", or one that is a branch of showbusiness.
It is because the Royal Family is in hock to the contradictory demands of public opinion that the Prime Minister's role as broker of the bargain is crucial. It was Disraeli who rescued Queen Victoria from her unpopularity by making her Empress of India in 1877 and identifying her with buoyant Imperial sentiment. It was Baldwin who had to tell Edward VIII what the British people would not put up with. This week it fell to our new, young and untested Prime Minister to guide the monarchy through a comparable crisis. There is no policy in Labour's manifesto, and he cannot have been prepared for this, but the advice he is giving in private could define his premiership.
In public, meanwhile, Mr Blair has so far contained the nation's ambivalence rather than resolved it. Before Diana's death, he appeared to be increasingly close to Charles, while his posthumous acclaim for Diana as the "People's Princess" appears to endorse many of her criticisms of what is by implication not a "people's monarchy".
He now faces the daunting task of advising the heir to the throne how to restore his family in the people's affections. But the death of Diana is far from the end of the monarchy in Britain. After all, she achieved all she did only because she was a member of it.
If nothing else, we should this morning remember her "destiny", as she described it in that last interview, which was to "try to help the most vulnerable people in society". It is Mr Blair's duty to help to ensure that her legacy is a more modest royalty, in both senses of the word, less emotionally repressed without sliding into American sentimentalism, and more evangelical about social justice.