But at the end of the programme, a newsflash came up, and Jennie Bond announced that Dando, the "ordinary but extraordinary" girl-next-door, was dead. Then, with the kind of ironic flourish that is a consequence of the weird fact-meets-fiction hyperworld of daytime television, Neighbours came on.
I went out to meet a friend who freelances for the Daily Mail. On the car radio as I made the journey, Jack Straw was making a statement to the House of Commons regretting the loss of Jill Dando. Tony Blair had already issued a statement. This also seemed strange for, although this death was a tragedy, it was not connected with the affairs of government. Anyway, the fact that this same Tony Blair had been arguing for days that the Jill Dandos of Serbia were legitimate targets in bombing attacks was a little jarring.
By the time I'd met my friend from the Mail, she'd already made the Crimewatch connection. We both felt sure that the murderer had been either a celebrity stalker or some other kind of loony who had been imprisoned due to the programme. Not random violence, then, but planned violence. Worse, more sinister, sicker. When I got home I learned that she may not have been stabbed, she may instead have been shot. By this time flags were at half mast, tributes were pouring in - not least one from the Queen - books of condolence had been opened, and flowers were piling up. And by this time as well, the first of many comparisons was being made with the death of Princess Diana, or with the murder of John Lennon. Tributes were arriving at the BBC website at the rate of one every two seconds.
A picture of a screen was flashed up on another screen, displaying the first of the messages. At the top was one from a woman who said she thought she had been desensitised to violence - until now. This seemed to me like a tribute no one would like to receive. Is the fact that this tribute has come from someone who has remained unmoved by war in Europe, nail bombs on ethnic communities in Britain, young lives blasted away in distant schoolrooms, supposed to enhance its value? Or does the fact that the murder of a television presenter is found to be more moving than any other death, instead demean us all?
And another picture was emerging on our television screens, a picture that was new to me. I didn't watch Holiday, or Crimewatch or Songs of Praise. I hadn't seen the first episode of Antiques Inspectors. I don't read OK! or Hello! or Radio Times. I'd never read an interview with Dando or an item of celebrity gossip about her. I'd never felt her warmth ooze into my living room, or made a personal connection with her through the machine in the corner. All of the details about her life and work that were flooding into my head were new.
The man for whom Jill Dando really was the girl-next-door had been on television, explaining how he had found her, unconscious and covered in blood, on their shared doorstep. Her brother, Nigel Dando, also a journalist, came on to say how shattered he was by her loss. Many other newscasters and television presenters, who were her friends as well as her colleagues, appeared on television to speak about their own sense of loss.
And they were united in all that they said. Jill Dando had been open, friendly, compassionate, professional, modest, without snobbery, caring, loving, close to her family, a good friend, a good colleague, a good neighbour. She had been beautiful, unaffected, intelligent, warm, thoughtful, sensitive, happy, positive, optimistic, charming, unassuming.
She had been preparing for her marriage, looking forward to starting a family. She had been a committed Christian, an enthusiastic and diligent charity worker, a loving daughter and sister. She had felt herself to live life on borrowed time for, as a child, she had had a hole in the heart operation. She had been slated as one of the presenters of the BBC's millennium coverage, while her first job, as a reporter on the Weston Mercury, had been secured after she wrote a 500-word essay on the year 2000. Of course, she has not lived to usher it in.
All of this makes her murder seem all the more poignant, even though we know that anyone's murder, whatever their flaws, is equally terrible. And while few people could have watched all of the tributes on television without weeping, my own tears made me feel ashamed.
What could these sentimental tears mean, in comparison to those of Jill Dando's fiance, Mr Alan Farthing? He has lost his love, his future, the children he may have had. He has lost her real presence in his life. Her physical warmth, palpable beside him until yesterday, no longer exists.
How do my tears match up to those of Mr Jack Dando, her father, who held her in his arms as a baby, who brought her up so well, who has lost his wife and now has lost his child? How will he live without her? Is our loss at all comparable to his loss?
How can all these people who feel that they know Jill Dando know her like her brother does, miss her like he does? How many times, as his life goes on without her, will he regret that there are joys and sadnesses he can no longer share with her?
And anyway, is the grief of fathers, brothers, fiances , friends greater because the loved one they have lost is "a woman who had everything"? For there is something disquieting in this too, as there was in the public reaction to the death of Princess Diana. Are nice, decent people this rare, that it is a national, not a personal tragedy, when one is lost?
Why do we feel the need to display our sadness so openly, with such presumption? We should all know that our own feelings of sadness are of a different, lesser order to those of the people who really did know her. We do not "know how they feel". We only imagine that we do. To claim a personal sense of loss, when we do not know this person at all, is surely self- indulgent.
Both the BBC and ITV broadcast tribute programmes after their early-evening news programmes, as much because this was the loss of someone many of them had known personally as because of the inherent news value of what, at this time, remained the kind of death that could befall any one of us.
But it was during the ITN tribute, led by Trevor McDonald, that the results of the post-mortem became public knowledge. Jill Dando had been shot in the head. Immediately, one's thoughts turned to the idea of a hitman, a contract killer. The prospect that Jill Dando's life was taken in exchange for money, as a consequence of her television appearances, is truly revolting. The police remain non-committal about connections to Crimewatch, but have said that because of that connection they look on the investigation of Jill Dando's murder as "one of their own".
This, again, I find to be very far from a fitting tribute. Late last night, there were news pictures broadcast of Jill Dando's Fulham home, cordoned off by the police with a shroud of white tarpaulin. News reports assured us that they were searching every inch of the crime scene for forensic evidence.
This reminded me of the death of another person who was said to be a decent, loving human being with a bright future ahead of him. But when Stephen Lawrence lay dying, no police officer even checked to see if the pool of blood he was lying in was coming from him. There was no tarpaulin shroud for him. The wife of an off-duty police officer cradled Stephen Lawrence in her arms while they waited for an ambulance, and whispered to him "you are loved, you are loved".
This wise, compassionate woman spoke the truth more accurately than she could have known. It is because Stephen Lawrence was loved so much that we have heard of him at all. But we have heard of Jill Dando because she had a successful career in television. And while we may now feel like yelling that we loved her, that doesn't make it true.
Whether it was a stalker who killed Jill Dando, or a contract killer, the likelihood is that she died as a direct consequence of her fame. The silly sentiment that makes television viewers feel that they knew her is not so different from the corrupted obsession that ended in blame and hate and murder.
The power we invest in celebrity, the significance we imbue it with, and the uniqueness we project on to those in the public eye, is dangerous in itself. We feel we have a right to make these investments, and talk quite casually about the price of fame. When we talk of this, we are often referring to the negative impact that fame often has on celebrities - the drink, the drugs, the neuroticism, the monstrous egotism, the lack of privacy, the failure of relationships and so on. We talk of these "prices" as if we have the right to charge them, as if they are assumed to be worth paying. Jill Dando was not paying any of these prices. She was normal, well-adjusted, happy. And instead the price of her fame has been the ultimate one. Surely, in our celebrity-obsessed, intrusive, prurient culture, there is something to be learned from this.