I was there. I remember thinking as I walked around that a very strange atmosphere prevailed. I wrote to family back home in Australia about it. Of course, with the exception of the murder of Lord Mountbatten, nothing like this had ever really happened to a Royal before. It was the most tremendous shock to everyone, the BRF, the Spencers, those that knew Diana, those that didn't. I think shock drove a lot of the opinions and reactions of people at the time.
No-one expected a beautiful and vital young woman of 36, a mother of two young sons, to die suddenly and horribly as she did. Members of the media were just as shocked, and reacted to possible attacks on them by turning on the royal family. I can remember people afterwards saying "Im never going to buy a women's magazine again" because of the way the papparazi and Press had behaved.
As I've said, I walked around central London for the week of the funeral for several hours almost every day. I heard people say various things about Charles, to the effect that if he had tried harder and given up Camilla, if he had been kinder, then Diana wouldn't have been in Paris that night, wouldn't have died. Illogical, perhaps, but that's the way people thought.
I never heard any of the complaints about the Queen being away at Balmoral, not at Buckingham Palace, made much of by the media, or attacks on the Queen being absent at all, except for one man who stated that he wished the queen was in London 'to see all this' (the flowers etc.)
I never saw any baying for blood, any desire to see the Queen 'pay' for Diana's death. I think the papers did try and play up a feeling of a lack of concern on the royals' part. This may have been felt among some of the populace but not expressed. I don't know but I didn't hear anything of that sort.
As I've posted before, there was undeniable grief, sorrow that this young woman had her life prematurely ended, and great concern for William and Harry's welfare, a feeling that has lasted, I think. In a way, people thought of the boys as members of their own families. These were the predominant feelings I remember and they were heartfelt, not media driven.