I think a full analysis of the public response to her death would need to go beyond the field of history and deep into the fields of sociology and psychology. From a historical perspective, though, I'd say that the most significant element was her place as an outsider in the Royal Family, and the way that public perception of the British monarchy had changed so dramatically over the 20th century.

If we look back to the early part of the 20th century, the monarchy was a fundamental pillar of British identity. The notion of service to 'King and Country' was central to recruitment and morale during the First World War; at the outbreak of that war, and at the Armistice, huge crowds gathered outside Buckingham Palace to sing 'God Save the King'. Similar scenes were seen at the end of the Second World War, with the Palace (and the Royal Family) again being a focal point for celebrations. The popularity of the monarchy was cemented by that conflict, in no small part by the Royal Family's refusal to leave London during the Blitz. Hitler reputedly called Queen Elizabeth (mother of the present Queen) "the most dangerous woman in Europe" because of her status as a much-loved figurehead; in 1941 Churchill wrote to George VI and Elizabeth:

This war has drawn the throne and the people more closely together than ever before was recorded, and your Majesties are more beloved by all classes than any of the princes of the past.

This isn't to say that there was universal fawning adoration of the Royals - historian Lucy Moore asserts that Elizabeth was jeered by crowds and pelted with rubbish during visits to bombed areas early in the war - but they occupied a central and critical position in the British national psyche, an embodiment of tradition, consistency and stability. (You'll have to excuse the focus on the world wars here as that's my area of interest; I expect others could give better examples!)

We can see this begin to dissipate as Britain moved into a post-Imperial future after the war, though. While street parties were held across the country for Queen Elizabeth II's Silver Jubilee in 1977, in the same year God Save the Queen by the Sex Pistols was released and hit #1 on the NME charts, a song intended to "evoke sympathy for the English working class, and a general resentment towards the monarchy." Towards the end of the 20th century, public support for the Royal Family began to slip sharply. Polls conducted by ICM Research for The Guardian newspaper in the early '90s showed that "70 per cent of respondents felt the country would fare worse without the Royal Family"; this dipped to 48% in 1997, just before the death of Diana, and had fallen to 44% in 2000.

Exploring the reasons for this is a huge subject in its own right, but the consensus seems to be that the wave of scandals, affairs, divorces and media exposés surrounding the Queen's children and their spouses (including Charles and Diana) through the early '90s are at the heart of it. The media were having something of a field day with the royals in the mid-90s, with televised interviews between Prince Charles and Jonathan Dimbleby in 1994 where he confirmed his extramarital affair, and between Diana and Martin Bashir in 1995 where she famously stated (referring to Charles's affair with Camilla Parker Bowles):

"Well, there were three of us in this marriage, so it was a bit crowded." Of herself, she said, "I'd like to be a queen of people's hearts."

So by the mid-90s the private lives of the younger royals were becoming rather a soap-opera in the press, and the former deference of the media towards royal privacy that was common in the earlier part of the century had largely evaporated. As the popularity of the monarchy amongst the public was on the wane, much public sympathy was extended to Diana (who had always been a fairly popular figure) as she was pushed to the outer fringes of royal life.

That's some of the historical context; as to why there was such an incredible public response to Diana's death, again I think that gets into the realm of mass psychology and sociology. I'd argue that the much-changed relationship between the media and the royals, and the corresponding presentation of Diana's life as a story that could be followed in the press, with her on one side and the increasingly-unpopular royal establishment on the other, was a very major factor.

Apologies for being a bit woozy on the sources, I'm mainly referencing from memory A Classless Society: Britain in the 1990s by Alwyn W Turner but also the diaries of Tony Blair and Alastair Campbell.

Princess Diana was the first member of the royal family (in its looses possible term, as she wasn't technically a royal after the divorce) to exist in the celebrity sphere that we'd now recognise. The courtship and the marriage were a huge media event, she was a fashion icon, and she made a conscious use of the media as a tool during her divorce and the aftermath to construct an image (accurate or not, I won't weigh in) as the wronged party and the victim, a humanitarian crusader, and a friend of the stars. Even her funeral was broadcast live.

Blair wrote in his memoirs that Diana "captured the essence of an era and held it in the palm of her hand. She defined it."

To look at Diana as a cultural icon in the mid-90s, we also have to consider the cultural groundswell of 'Cool Britannia' - there was an enormous sense of energy and momentum about the way Britain presented itself to the world, from the youthful sincerity of new Prime Minister Tony Blair, to the swagger of Brit Pop, to Hugh Grant waffling through whatever it is his films were about, to the Spice Girls' laddette feminism. Princess Diana firmly fit into that pantheon and she occupied a key role.

We've had princesses before, we've had bleeding hearts touring the world before, we've had high profile divorces before, but none of this had happened to an institution with the cache and fascination of the Royal Family.

Britain in the 90s was suddenly very class conscious. The traditional class lines had been eroded by, among other things, the decline of the organised labour movement after a series of confrontations in the previous decades, the 'new money' of the Yuppies, and the expansion of home ownership to council tenants. The antiauthoritarianism that had been underground in the 80s had also been co-opted by the mainstream, punk had effectively become Geri Halliwell's union jack dress as she pinched Prince Charles's bum.

What this meant is that the traditional barriers of class were now much more fluid and that traditional deference to the monarchy, and indeed all institutions, had faded. The monarchy were increasingly being viewed in human terms, not as an embodiment of the nation, and Charles and Diana's marital discord was preceded by a series of scandals that had created a tabloid interest in the inner workings of the house of Windsor, including Prince Andrew's separation from Sarah Ferguson and the fire at Windsor Castle in 1992, the latter resulting in both the demystifying footage of priceless artefacts being ferried from this crumbling edifice and the the unedifying conversation of who exactly would be paying for the restoration. The end result being that the Queen agreed to pay income tax and Buckingham Palace being opened to tourists.

It's not quite the royal family being thrown into the street but the 1992 Windsor fire is a good example of reality intruding into the isolated, protected sphere of the monarchy and the limits of political and public indulgence. I'd argue that as much as the Prince Andrew/Sarah Ferguson divorce, it helps explain why Princess Diana was seen as being a moderniser and a rebel, and why she was able to solicit both so much empathy and so much hostility.

Sarah Ferguson was also an interesting precursor in that, although portrayed very differently in the press that mocked her crassness and entitlement, her story played out in front of the long lenses, creating a boom town for gossip that Diana inherited. It's no coincidence that Sue Townsend's satirical novel, The Queen and I, imagining a republican Britain forcing the royal family into a council estate, came out the same year as Fergie was papped having her toes sucked by her lover at the poolside.

Mass outpourings of grief in Britain aren't as uncommon as a lot of the recent anniversary literature would suggest though. When Princess Charlotte died tragically in childbirth in 1817, shops closed for two weeks and there was a cottage industry in mawkish poetry. The future Lord Chancellor Henry Brougham observed: "It really was as though every household throughout Great Britain had lost a favourite child."