Courtesy :http://www.bbc.co.uk/news/health-24063286
Experts looked at data on 10,000 children diagnosed under five between 1962 and 2007, and where they lived.
The British Journal of Cancer study is not the first to rule out a link - but previous studies' methods were challenged.
Cancer Research UK said the results were "heartening" but added monitoring should continue.
Leukaemia is the twelfth most common cancer in the UK, but accounts for a third of all cancers diagnosed in children.
Around 500 new cases were diagnosed in children under the age of 15 in 2010 in the UK.
Concern over a link between nuclear power plants and childhood cancers was triggered in the early 1980s when a TV investigation reported a higher number of cases among children living near the Sellafield plant in Cumbria.
Since then, there have been conflicting reports from studies in the UK and the rest of Europe as to whether there is a link.
Some anti-nuclear groups have criticised the way previous studies have been carried out.
They point to a German study which suggested there could be a link.
'No correlation'
In this latest study, carried out using the same method as the German one, experts from the Childhood Cancer Research Group in Oxford looked at data on almost 10,000 children who were diagnosed with leukaemia or similar cancers in Britain between 1962 and 2007 when aged five or under.
The data was taken from the National Registry of Childhood Tumours, which has kept records on nearly all children diagnosed with cancer since 1962 and which is linked to birth records for children born in Britain.
They looked at where these children were born and where they lived when they were diagnosed.
They also compared the information with data on more than 16,000 children with different cancers.
The study found there was no apparent increased risk of developing childhood leukaemia or non-Hodgkin lymphoma among children living near nuclear power plants.
Dr John Bithell, honorary research fellow at the Childhood Cancer Research Group who led the study, said: "The incidence of childhood leukaemia near nuclear installations in Great Britain has been a concern ever since the 1980s when an excess of cancer in young people near Sellafield was reported in a television programme.
"Since then, there have been conflicting reports in the UK and Europe as to whether there is an increased incidence of childhood cancer near nuclear power plants.
"Our case-control study has considered the birth records for nearly every case of childhood leukaemia born in Britain and, reassuringly, has found no such correlation with proximity to nuclear power plants."
Cancer Research UK said the study did support previous findings, but said its small numbers and the fact it did not look at plants which carried out other work such as fuel processing - plus the finding of an increased risk in the German study - meant more work was needed.
Hazel Nunn, head of health information, said: "It's heartening that this study supports the findings of the Committee on Medical Aspects of Radiation in the Environment (COMARE), that being born or living near a nuclear power station doesn't lead to more cases of leukaemia and similar cancers in children under five in the UK.
"But these results can't rule out any possible risk, so it's still important that we continue to monitor both radiation levels near nuclear power plants and rates of cancer among people who live close by."
