Instead Sir Keith Ajegbo believes pupils should be taught about the experience of living in the UK and devise their own versions of what Britishness means. His review found that citizenship lessons were patchy.
It calls for more training and resources for teachers, a new citizenship GCSE, and for all schools to teach citizenship as a distinct subject and to ensure that diversity is taught across the curriculum.
The review was commissioned as part of the Government's response to the July 7, 2005 bombings, when ministers said they wanted to look at how British values could be underpinned in the citizenship curriculum.
Gordon Brown has made "Britishness" a key theme as he prepares to take over as Prime Minister. But Sir Keith told The TES: "We felt it should be about the experience of living in the UK as opposed to calling it Britishness.
That Britishness for some people might be seen as difficult to define and contentious."
Asked he if was rejecting the idea that a particular set of values should be defined as British, he said: "Yes. If you are looking at it as a British Muslim or as an Afro-Caribbean child then their history and their interpretation of some things will be different."
Sir Keith wants a new fourth strand to the citizenship curriculum called Identity and Diversity: Living Together in the UK to encourage critical thinking about religion and race. It would also include learning about history and politics and cover the Commonwealth, the legacy of Empire, the European Union and the UK's four nations.
A critical Ofsted report on citizenship lessons in September found they were not good enough in a quarter of schools with some barely teaching it.
Sean Lang, who is chairing a Conservative advisory group on history, said that a better response to the London bombings would be to re-think the history curriculum to teach pupils about Britishness and the political side of citizenship. Other aspects could be included in personal social and health education.