Comare, a committee set up to advise ministers on the effect of radiation exposure, studied 32,000 cases of childhood cancer from 1969 to 1993.
It suggested the finding could be related to an immune system response to infections which was more likely in less densely populated areas.
But it said cases of lymphomas showed the opposite trend.
For many of the other childhood cancers, including tumours of the nervous system and soft-tissue sarcomas, there was no demographic trend.
About one in 500 children develop some form of cancer before the age of 15.
The study, the largest of its type ever carried out, also found that all childhood cancers do not occur evenly across Britain.
The researchers said the variations were greater than could be explained by pure chance and had to be caused by some other factors.
Comare chairman Professor Alex Elliott said the report raised a “whole host of questions” that required further research.
“It is not clear why childhood cancers tend to cluster like this.
“Much attention has been given to interactions between exposure to infections and immune responses.
“Other possible explanations have also been considered, including exposure to environmental agents.”
But researchers said no general pattern of increased cancer incidence was seen around nuclear plants with the exception of Sellafield in Cumbria and Dounreay in Scotland – both of which were already known about.
When the clustering of childhood cancer was looked at among social demographic groupings, the highest rates were seen in the two most affluent groups.
They had rates of 39.6 cases per million and 40.9 cases per million compared to 36.4 cases per million for the most deprived group.
It meant that relatively affluent areas such as Buckinghamshire, Cornwall, Dorset, Kent, Surrey and Wiltshire had leukaemia rates much higher than the average of 37.7 cases per million.
A similar, albeit slightly weaker, pattern also emerged for bone tumours.
The report said there was no clear reason for the findings, but said one theory was that an immune response to infections could act as one of the triggers for leukaemia and this was more likely in richer areas.
It said more affluent parts of the country tended to be the least densely populated and this meant that in the first years of life children did not mix with other children as much as their counterparts in more deprived areas.
It added, as a result, the immune system developed less – the so-called “dirty hypothesis”.
However, the report said it was also possible that the higher rates could be attributed to better diagnosis.
A Department of Health spokeswoman said: “This is an important finding and could lead to a better understanding of the causes of such cancers.”
But the Health Protection Agency said there was no current consensus for the clustering.
“It may lend weight to the hypothesis that common infections may have a role in initiating or promoting the growth of cancer cells, assuming cancer is a multi-stage process.
“However, it is also possible that some local environmental factors could be involved.”