It was strange, reading a rather old-fashioned book to my children the other night, to come across a description that I understood exactly, but realised would mean nothing to them. Harriet, in Noel Streatfield's White Boots, had been ill and was supposed to be recovering, but she still felt "so cotton woolish and all-overish that she had not really got the energy to argue".

It brought back to me instantly the horrible, lingering feeling of sickness, where you turn hot and cold and the bed feels hard and lumpy, but your legs wobble if you get out of it and you can't wait to lie down again. And it goes on like that for days. And the wallpaper makes you hallucinate. And your mum brings you a tray of lunch in bed and you can't do more than pick at it because your throat hurts and you're not hungry and anyway it tastes peculiar.

I was not an unusually sickly child. These sorts of bouts were normal. I had the childhood diseases of the day - measles, German measles and a rather unfortunate combination of tonsilitis, followed by tonsil extraction, followed by chicken pox caught in the hospital.

Maybe my own kids are luckier. One is seven and the other is nine and they've never spent a day in bed in their short lives. Within a generation, children's health has changed dramatically. Today's kids don't get those nasty, lingering and potentially dangerous diseases, thanks to mass-vaccination programmes against measles, mumps and rubella (German measles). Mine are also well-nourished and live in a house with adequate heating and ventilation and no damp. According to Nigel Klein, consultant in infectious diseases at Great Ormond Street, better living conditions ensure secondary infections following minor diseases such as chicken pox are a lot less common and so is bronchitis. There are still too many children who live in sub-standard housing and whose health may not be so robust, but on the whole, the old familiar childhood illnesses have lost their scariness.

There may be a price to pay for the annihilation of all those bacteria and viruses that used to invade children's bodies and cause disease. There are theories that young immune systems are not now being primed as they used to be to fight infection, which may be a cause of the increasing incidence of allergies and asthma. But children no longer die of measles, at least while the vaccination rates remain high.

Parenthood and anxiety going together like the proverbial horse and carriage, the disappearance of ordinary childhood ailments creates a vacuum that something else must fill. Far rarer diseases scare the living daylights out of parents today, such as meningitis (even though vaccination for the C strain has cut the risk), leukaemia and now tuberculosis.

But in fact, worries about disease are pretty much misplaced in the UK. The biggest killers of children are accidents. There are 500 child deaths a year in accidents - with traffic accidents as the lead cause of mortality followed by fires.

The UK has one of the worst records for child deaths in road accidents in Europe - higher than France, Spain and Italy. Teaching children to cross the road safely has little benefit compared with tackling the motorist. Clamping down on drink-driving, putting humps in roads to cut drivers' speed and seat belts all help reduce the dangers. There are well-tried and tested ways of reducing the risk of fire, too - particularly by the installation of smoke alarms in homes.

These things work, but they are far more likely to be found in affluent areas than in poor areas. And sure enough, most of the children who die in accidents are poor. Poorer children are eight times more likely to be killed by a car and 15 times more likely to die in a fire.

The government has promised to tackle accidents as one of its priority areas. It has also pledged to stamp out inequalities in health. There isn't a cheap, universal vaccine to keep seven year-olds from being hit by a speeding car as they play in the street because they haven't got a garden. It's poverty that has to disappear, and that will take more than the few years it took to stamp out those childhood infections.