CND chairwoman Kate Hudson has launched an email campaign targeting Defence Secretary Liam Fox and Defence Minister Nick Harvey after the government said there would be no compromise over Trident.
"I am very relaxed about explaining to our Liberal Democrat colleagues that the system is actually the best value for money," Mr Fox said.
"We believe that Britain needs a credible nuclear deterrent."
But Ms Hudson retorted: "Many voters who were engaged by the Trident debate in the election will be desperately disappointed that the Tories' pro-Trident policy holds sway.
"Those voters opposed to Trident replacement will have little confidence that the Lib Dems will impact on the government's direction.
"They have not even secured a commitment to including Trident replacement in the Strategic Security and Defence Review.
"President Obama campaigned for change and is going forward on this issue, delivering cuts in US nuclear warhead numbers. I'm afraid our new government is going nowhere."
The replacement of Trident is a proposal to upgrade the existing Vanguard class of four submarines each armed with 16 Trident II submarine-launched ballistic missiles.
The government has begun planning a new submarine-based system but there is opposition from those who want to take the opportunity for full nuclear disarmament or replacement with a cheaper, less capable nuclear weapon delivery system.
The CND email campaign is calling on Mr Fox and Mr Harvey to include Trident in the government's Strategic Security and Defence Review.
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