Thom Yorke, lead singer of rock group Radiohead, joined hundreds of campaigners at a US defence base on the North York Moors on Saturday.
The CND protest highlighted the group's opposition to the US 'Star Wars' missile defence system, of which the Fylingdales base is part.
Campaigners say President Bush is expected to announce that phase one of the project is up and running.
The chair of CND, Kate Hudson, was also among 350 participants.
Among the crowd were supporters from Japan who travelled to the UK specifically for the event.
'Pleasant and peaceful'
Neil Kingsworth, of Yorkshire CND, said: "It's been a brilliant atmosphere, pleasant and peaceful yet lively at the same time.
"A lot of people came because of Thom Yorke and it's wonderful that someone like him will take on such a complex issue.
"He told everyone how important it was for them to attend these protests and to keep plugging away as he cannot understand what right America has to be the policeman of the world."
Police confirmed that no-one was arrested and there had been no trouble.
'Control in peacetime'
The Radiohead singer had written a message on the band's website urging people to join the protest.
Ms Hudson said: "This is an offensive rather than a defensive system.
"The reality is that missile defence is about control in warfare and control in peacetime.
"It is about making wars like that in Iraq easier to start and easier to win."
The demonstration was held on the first day of the international "Keep Space for Peace" week.
Mr Kingsworth said: "This action is taking place at a crucial moment at the key Star Wars site in the UK.
"Bush's plans to announce the start of Star Wars this autumn, bringing the threats of nuclear proliferation on Earth and a space weapons race in space closer to reality.
"If we allow the UK to keep supporting Star Wars then this country will become complicit in the development and deployment of space weapons - a whole new type of battlefield - and the creation of a system for nothing more than control and dominance."