"The evidence from many countries persistently shows that children who grow up in poverty are more vulnerable," the report said, especially in terms of academic underachievement, chances of unemployment and low self-esteem.
Child well-being was rated highest in northern Europe, with the Netherlands, Sweden and Denmark leading the list.
"All countries have weaknesses that need to be addressed and no country features in the top third of the rankings for all six dimensions," David Bull, the UK executive director of Unicef, said.
Britain lived up to its reputation for "binge-drinking," hazardous sexual activity and drug use, with the report putting the country at the bottom of the rankings for risk behaviours "by a considerable distance".
Almost a third of British youngsters aged 11, 13 and 15 reported being drunk on two or more occasions, against just an average of under 15 per cent in the majority of countries in the Organisation for Economic Co-Operation and Development.
Britain had made progress in the field of child safety, having cut the incidence of deaths from accidents and injuries to the "remarkably low level" of fewer than 10 per 10,000.
Sweden, the Netherlands and Italy also achieved the same rate of progress.
Britain and the US were also found to have the worst rankings in terms of children's relationships with their families and peers.
Unicef noted the sensitivity of this field, but said "at the statistical level, there is evidence to associate growing up in single-parent families and stepfamilies with greater risk to well-being," including dropping out of school, leaving home early, poorer health and low pay.
The US, Britain and Sweden had the highest proportion of children living in single-parent families, while Italy, Greece and Spain had the lowest.
The study, which looked at 40 indicators to gauge quality of life in economically advanced nations, is the first of its kind.
The report said no direct link had been found between gross domestic product and children's well-being.
It highlighted how the Czech Republic had a higher ranking than many richer countries, including France, Austria, the United States and Britain.