According to the ESRC Research Centre on Dynamics of Ethnicity, 4% of all people chose a different ethnic group in the 2011 Census than they had in the 2001 Census.
Professor Ludi Simpson said "Ethnicity is a fuzzy concept used by government and sociologists to explain and support the diversity of our society. But as individuals we don't fit into neat boxes.
"The census form itself changes and encourages people to swap ethnic identities. 26% of White Irish changed their ethnic group from 2001, partly because the census form in 2011 added a note that mentioned that White British could include Northern Irish."
The research was jointly funded by the University of Manchester and the Joseph Rowntree Foundation. It is published in a Census Briefing and a working paper, which note that the level of instability in the past decade 2001-2011 is twice what was observed for the decade 1991-2001.
Professor Simpson added: "Britain's growing diversity includes more people whose family background does not fit neatly into one category. This is partly because of immigration from new parts of the world. It is also because we have grown used to defining ourselves by this thing called ethnicity, and more of us are no longer satisfied with the options provided on the census form. We more often write in our own sense of identity."
The new research recommends the ethnic group categories that can be most reliably compared across the 1991, 2001 and 2011 censuses.
Explore further: A bigger melting pot: What the census really tells us
The census briefing is available online: www.ethnicity.ac.uk/census/CoDE-Changing-Identities-Census-Briefing.pdf