The vast majority of child deaths occur in developing countries
The UK is lagging behind other high income countries on cutting child mortality, international figures show.
Along with the USA, New Zealand and South Korea, child deaths in the UK have not fallen as quickly as expected.
The research confirms the UK has the highest child mortality rate - 5.3 per 1,000 live births - in Western Europe.
But new global estimates published by The Lancet show that in many poorer countries, the decline in deaths in the under-fives is speeding up.
The analysis done by a team at the University of Washington in Seattle found stark differences in child deaths between high-income countries.
As well as having the worst child mortality in Western Europe, globally the UK fell from 12th best in 1970 to 33rd best in 2010.
The UK has reduced its mortality by three quarters since 1970, and by almost half since 1990, but Austria, Belgium, Cyprus, Germany, Greece, Ireland, Israel, Italy, Luxembourg, Malta, Portugal and Spain have all overtaken the UK in the past four decades.
Overall, the researchers found that deaths in children under the age of five are actually lower than the latest estimate provided by Unicef.
Worldwide mortality in children younger than five years has dropped from 11·9 million deaths in 1990 to an estimated 7·7 million deaths in 2010.
A third of those deaths occur in south Asia and half occur in sub-Saharan Africa.
The researchers said the latest data show that cuts in child mortality have been faster than projected in many poorer countries.
In 13 regions of the world, including all regions in sub-Saharan Africa, the figures suggested faster declines from 2000 to 2010 compared with the previous decade.
Study leader Dr Christopher Murray said the apparent acceleration of progress in poorer countries was encouraging evidence that it was worth intensifying efforts further.
He said improved education for women, the lessening negative impact of HIV, and expansion in programmes such as bed nets and vaccination had all played a part in the improvements seen in developing countries in the past decade.
Dr Murray agreed that the UK had seen a "big slide" in its ranking in terms of child mortality.
"When you get to these low levels of child mortality seen in high income countries, healthcare probably is an important component in the variation.
"Most of the deaths in places like the UK will be neonatal and you would have to look in more detail at what aspects of healthcare might explain that difference."
A Department of Health spokesman said infant mortality in the UK is at its lowest ever level.
"However, the death of any child is one death too many and we must continue to do all we can to prevent those we can.
"This is why every child death is now subject to a detailed review to understand why children die and what steps can be taken to protect other children."