Three families had brought the case on behalf of their children in north-east London where the National Grid has laid six 275,000-volt cables between Tottenham and Redbridge.
The parents fear the increased electro-magentic field could increase the risk of childhood leukaemia and other cancers up to six times.
In what was seen as a test case Lloyd Duddridge, aged seven, Danielle Bye, five, and Naomi Holliday, three, acting through their fathers, sought court orders requiring Mr Heseltine to protect the public and ensure that electro- magnetic fields from the cables do not exceed levels that research suggests are safe.
Lord Justice Farquharson and Mrs Justice Smith refused their application for a judicial review. Mrs Justice Smith said she had reached the 'clear conclusion' that there was no obligation for Mr Heseltine to apply the precautionary principle, under Article 130r of the Maastricht treaty which concerns the protection of human health and the environment.
She said: 'The status of the precautionary principle would appear to be no more than one of the principles which will underlie the policy when it is formulated.'
A spokesman for the Department of Trade and Industry, welcoming the decision, said: 'The court has accepted the president's decision was properly and validly taken. The applicants failed to show any ground on which the president's refusal to issue regulations may be impugned.
'The issue is one that ministers have always taken very seriously. We understand the concerns of parents and should any new evidence appear it will be considered carefully.'
The chief press officer for the National Grid, John Washburn added: 'We are pleased with the outcome of the court case. It now allows us to go ahead with a project we feel plays an important part in the security of the electricity system through the London area.'
He said there had been no causal link found between power lines and cancer but added: 'We are spending over pounds 1m a year in research into electro-magnetic fields and that will continue.'
Outside the court, Lloyd's father, Phil Duddridge said: 'We are bitterly disappointed - disappointed but not defeated. It is an issue which is certainly not going to go away.'
The family's solicitor, Martyn Day, urged the National Grid to delay switching on the cables on 14 October. He said: 'In my view there is clearly a moral duty, regardless of the legal position, for the Government to act as a matter of precaution. It is ludicrous they are prepared to gamble with people's lives.'
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