Black and Arab Britons are more than 40 percent less likely to own their own home, compared with white Britons, the report said.
The survey highlighted unemployment and huge disparity existed in ownership of houses in the country.
Mrs May, who commissioned the audit soon after becoming PM a year ago, has faced criticism that it describes the problems faced by Britain's ethnic minorities but does not include proposals to solve them.
It shows that black people were more than three times more likely to be arrested than white people, with black men nearly three and a half times more likely to be arrested than their white counterparts.
■ Around two out of three white British householders owned their homes compared with just two out five householders from all other ethnic groups combined.
■ Of all applicants shortlisted for NHS jobs in England, white candidates were more likely to be appointed - some 18 per cent of whites shortlisted got the job compared with 11 per cent of ethnic minorities.
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 "unprecedented" audit pulls together data on how people of all ethnicities are treated in areas including health, education, and criminal justice.
■ Households of Bangladeshi, Pakistani, black, mixed and other backgrounds were more likely to receive income-related benefits and tax credits than those in other ethnic groups.
British white groups also fall behind in some instances, the data showed, with white British pupils on school meals less likely to reach the expected standard at Key Stage 2 than any other ethnic group.
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).
"But this audit means that for society as a whole - for government, for our public services - there is nowhere to hide".
The Equality and Human Rights Commission called for a "coherent race equality strategy" from government.
The Prime Minister's recent rhetoric around race has attracted criticism, however.
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. "But the solutions the Government is putting up are little more than a plaster on a gaping wound".
Liberal Democrat leader Sir Vince Cable said the audit showed a prejudice that was "utterly unacceptable in 21st century Britain".
Martha Spurrier, director of civil rights group Liberty, said: "The bleak picture this report paints of racial injustice in the United Kingdom demands an immediate and bold response".
In a letter to The Times today, a number of prominent BAME activists - including former deputy mayor of London Munira Mirza - hit back at the government's "crude and tendentious" approach to the issue, saying the policies could "harm the very communities they aspire to help".
"The findings from the Race Disparity Audit present us with a real opportunity to make transformative change in tackling persistent race inequality", said Simon Wooley, Director of Operation Black Vote, following the report's publication.