The group asked the court to declare that it would be contrary to international law for the UK to go to war against Iraq without a fresh United Nations resolution.
CND claims a UN resolution calling on Saddam Hussein to disarm or face "serious consequences" cannot be used to justify an invasion.
The campaign went armed with legal advice from a top QC from human rights firm Matrix Chambers, of which Cherie Blair is a member.
'No trigger'
Rabinder Singh QC told the three senior judges that UN Security Council Resolution 1441 set out Saddam Hussein's disarmament obligations, but did not authorise the use of armed force if it was breached.
The QC asked Lord Justice Simon Brown, sitting with Mr Justice Maurice Kay and Mr Justice Richards, to rule that CND had an arguable case which should go to a full hearing as a matter of urgency.
Mr Singh said: "If there is a war against Iraq without a fresh resolution and it subsequently turns out that in law there should have been one, it will literally be too late."
The UK was at the forefront of efforts to hammer out a new UN resolution demanding the disarmament of Iraq.
Resolution 1441, adopted on November 8, gave Baghdad, in the words of the resolution, "a final opportunity to comply with its disarmament obligations" and allow the weapons inspection teams to carry out their role.
Mr Singh told the court: "We intend to submit that it does not authorise the use of armed force against Iraq in the event of its breach."
Lord Justice Brown suggested to Mr Singh that, if the government believed "the national interest and security of the realm" depended upon an act of war - "irrespective of conformity with international law"- no court was going to say to it: "You can't."
Embarrassment
Legal action in a British court could not prevent US-led military action in Iraq.
The US is also unlikely to recognise the jurisdiction of the International Court of Justice in the Hague.
But court action by CND has the potential to cause embarrassment to the UK Government, which already has concerns about the legality of enforced "regime change".
Outside court, veteran former Labour MP Tony Benn, a long-time peace campaigner, said of Monday's challenge: "This has to be done because a world without international law would be back to the jungle - we simply can't allow that to happen."
He added: "If there is a victory in this one, it would really change the course of British politics."