But these were not avid Royalists, hysterics, or even Mills & Boon sentimentalists, looking desperately for emotional contact. Some of them I count as being among the most rational and level-headed people I know. So what force co-opted them into the National Grief?
Listening to their tales I was reminded of the characters from Spielberg's Close Encounters, who are drawn to the strangely shaped, isolated mountain in the American desert. The original lonely impulse to travel there surprises each one of them, they do not really understand the significance of the place, and they certainly do not know - most of them - that this is the chosen rendezvous for an encounter that is both historic and magical. But as they come closer, and discover others making the same inexplicable pilgrimage, they are comforted. They enjoy a contact, a common experience that they hardly knew they needed; a solidarity grows up among folk who hardly used to speak to their next-door neighbours. "It was really lovely to see everyone all together and all feeling the same," said a woman who had attended a special service in Canterbury Cathedral on Thursday night. Today millions will take part in the final stages of the collective action - and it is virtually impossible not to feel moved by it.
It is enormously tempting to describe this as some kind of mass pathology. Media shrinks can explain some of it in terms of the stages of the grieving process, or of hysteria. "I'd say, clinically, it's all a bit odd," was the reaction of Oliver James on Wednesday's Newsnight, before he was slapped down by the presenter for having said precisely what he was invited on the programme to say. And certainly the "sightings" of Diana's face in a portrait of Charles II haven't helped.
But I really don't think it is necessary to reach for our Freud when trying to understand what is going on here. We are not witnessing any frenzies; there is no flagellation, no persecution of the Jews, no rending of clothing or attacks on minorities. Rather, there is an enormous desire to be part of something bigger than ourselves, which links our quotidian experiences and emotions to those of others. It is - in a sense - the obverse of road rage, that anti-civil phenomenon born of paranoia and isolation. It is the excuse for smiling at perfect strangers, for crossing the boundaries of silence and suspicion that govern much of our lives.
It isn't new. In a minor way it happened very recently, when even those who care very little for football suddenly sported the cross of St George and knew the words to "Three Lions on a Shirt". Those who were alive for VE Day - when men and women fell into each other's arms all over Britain - can testify to other great moments of collective identification. We need to do it. Competition, continuous striving one against the other, or group against group, never was the whole story of humanity - particularly not for women.
That's why my usually monosyllabic African mini-cab driver told me - in a sudden burst of eloquence last night - that he would be standing on the route of the cortege, his young son's hand held tight, so that he too would be "a part of history". He, like millions of his fellow citizens, many of whom will never have met or spoken to a man such as he, will be together today, exercising power in the most unaggressive manner. You don't have to buy the hype to see that there is much here that is good.