The Prime Minister has committed to holding a debate in Parliament over the issue.
Beckett told the Sunday Times that it was the Cold War that prompted the Trident programme but that the security situation now is very different.
Though Trident is not due for replacement for 20 years, Tony Blair has promised that there will be decision on Trident this year, due to the long lead time for design and construction. The costs involved may be between 10 and 25 billion pounds.
Beckett said that the public should be informed and should think about the issue themselves.
Her opinion will be welcomed by back bench Labour MPs who are concerned that any opposition to replacing Trident will be suppressed.
Beckett has also taken an independent line before, on Iraq, by expressing 'regrets' over the war and saying she did not disagree with General Sir Richard Dannatt, who said that British troops in Iraq were provoking trouble.
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