The phrase "a movement based on" is correct and usable in written English.
It can be used to describe the foundation or principles that underpin a particular movement or initiative.
Example: "The environmental movement is a movement based on the principles of sustainability and conservation."
Alternatives: "a movement grounded in" or "a movement founded on".
Their efforts launched a global movement, one dedicated to the universal realisation of child rights -- a movement based on the sure and certain conviction that children not only have a right to a better future -- but that, in a quite literal sense, they are the future.
"This is a movement based on love".
"In the end the movement behind him is a movement based on him personally".
But a movement based on patriotism and Reagan-worship alone could not have spread so rapidly nationwide.
Spiritualism, in religion, a movement based on the belief that departed souls can interact with the living.
Can Labour build a movement based on hope and also ask itself some very difficult questions about 21st century Britain?
I see OWS as a patriotic movement, based on a deep and abiding love of country -- a patriotism that it is not just about the self-interests of individuals, but about what the country is and is to be.
Much to Frum's dismay (he acknowledges), American conservatism is at its core a cultural movement based on a vision (myth) of American-ness.
Modern marketing techniques could be used to promote a social movement based on an emotional and symbolic connection between improved preconception maternal health and nutrition, and offspring health.
Warren F. Evans (1817 89), a Methodist and then a Swedenborgian minister (leader of a theosophical movement based on the teachings of the 18th-century Swedish scientist and theologian Emanuel Swedenborg), published a number of works exploring and systematizing the ideas of Quimby.
