While 85% of white people reported a sense of belonging, 84% of Asian respondents and 81% of black people also agreed to strong feelings of Britishness.
The Prime Minister ordered an audit of the treatment of ethnic minorities after taking office past year with a promise to tackle injustices.
The report - covering health, education, and housing, for example - reveals that different groups fall behind in different areas.
Theresa May is to challenge society over differences in how public services treat people of different races.
Previously published data included in the new survey shows that black people are six times more likely than whites to be stopped and searched by police.
An external review will also be brought in to improve schools' exclusion policy, with a focus on ethnic groups disproportionately likely to be suspended or expelled.
"This and the higher chances of them falling victims to crime also has to do with the areas in which they live - ethnic minorities are more likely to live in deprived areas where there is more crime taking place".
But there are some areas where whites suffer worse than minorities - with white children more likely to claim free school meals and white patients worse hit by mental health problems.
Asian, black and other ethnic groups were disproportionately likely to be on a low income, with nearly half of households in the bottom 40 per cent nationally before housing costs were taken into account.
When it comes to employment, British Indians had among the highest rates of hourly pay, above the national average and the white British community, while levels of employment were only marginally lower than those of white British (73 per cent against 75 per cent).
Ethnic minorities are more likely to live in areas of deprivation, especially black, Pakistani and Bangladeshi people. White British adults were more likely to have suicidal thoughts, however.
"But this audit means that for society as a whole - for government, for our public services - there is nowhere to hide".
'But our concern is the way that the Government has framed these disparities as being about discrimination or racial injustice, implying that there is unfair treatment of ethnic groups when in fact there are many different complex reasons why ethnic groups have different outcomes'.
The Equality and Human Rights Commission called for a "coherent race equality strategy" from government.
Meanwhile, Labour have accused Theresa May of adding "fuel to the fire" instead of tackling "burning injustices" as the findings of the audit were released.
Liberal Democrat leader Sir Vince Cable said the audit showed a prejudice that was "utterly unacceptable in 21st century Britain".
"The bleak picture this report paints of racial injustice in the United Kingdom demands an immediate and bold response", she said.
The figures have prompted demands for the Government do more to tackle the inequities.
"While we welcome the publication of this data, and the Prime Minister's commitment to "explain or change" the disparities it highlights, this must now be accompanied by the resources and action necessary to make a real difference". Former Deputy London Mayor Munira Mirza said the project risked stoking a "grievance culture".