The Campaign for Nuclear Disarmament (CND) has welcomed Ed Miliband's statement that alternatives to Trident must be considered.
But while a review of alternatives is a "step forward" for the party which initially pushed for Trident replacement, Miliband did not mention the possibility of "a future without nuclear weapons" said CND's Kate Hudson.
Challenged in a Q&A at Labour Party Conference on whether he would commit over £100 billion to Trident replacement, Miliband said that alternatives should definitely be considered, while appearing to echo the Lib Dem policy of retaining some form of "minimum nuclear deterrent".
The statement comes in the same week that Shadow Defence Secretary Jim Murphy said Labour would discuss Trident when the outcomes of the Lib Dem-Led Trident Alternatives Review are published early next year - a review which remains committed to some form of nuclear weapon system.
CND General Secretary Kate Hudson said "It should be welcomed that the Labour Party is no longer wedded to one particular system - and a review into alternatives is a step forward - but any review must also consider a future without nuclear weapons."
"Labour should not wait for their cue from the Lib Dem's Trident Alternatives Review, which has also shied away from considering the option of non-replacement."
"Senior military figures are decrying the government's commitment to Trident replacement on strategic and economic grounds.The British public are opposed to £100 billion going on a Cold War weapons system at a time when public services are being slashed.
"And former Defence Minister Nick Harvey has just said that there are now very serious questions being asked in Whitehall about replacing Trident."
She concluded: "Labour cannot afford to support this deeply unpopular, strategically useless and economically catastrophic weapons system."