Launching a new website - called Ethnicity Facts and Figures - May said she wanted to bring about a change in attitude across society, including health, education and the criminal justice system so that everyone is treated equally.
The website assembles both new and already published official data on racial disparity in one place for the first time.
Among findings are that white and black pupils, particularly those who are eligible for free school meals, are falling behind their peers at school.
Just 54 per cent of white British pupils, 51 per cent of black children and 13 per cent of white Gypsy and traveller children reach the expected standard for reading, writing and maths at primary school. In contrast, 71 per cent of Chinese pupils are reaching this level.
Regional variations are also exposed in the audit, with more than three quarters of black primary school children reaching expected academic levels in Sunderland and Gateshead, compared with less than a quarter in Stockport.
Among action pledged by government includes a review by the Department for Education to improve practice in school exclusions.
"This will share best practice nationwide, and focus on the experiences of those groups who are disproportionately likely to be excluded," a government statement added.
DfE figures published in July show that black Caribbean pupils were more than three times as likely to be permanently excluded than the school population as a whole, while Chinese and Asian pupils had the lowest rates of exclusion from school.
The move coincides with a report published today by the Institute for Public Policy Research that calls for the best teachers to be encouraged to work in pupil referral units to support this group of vulnerable children.
Other action includes a targeting of 20 racial disparity employment "hotspots" by the Department for Work and Pensions, which may include an offer of traineeships for 16- to 24-year-olds from ethnic communities.
"People who have lived with discrimination don't need a government audit to make them aware of the scale of the challenge," May said.
"But this audit means that for society as a whole - for government, for our public services - there is nowhere to hide. These issues are now out in the open.
"And the message is very simple: if these disparities cannot be explained then they must be changed."
Chris Keates, general secretary of teaching union NASUWT said that racial disparity in schools also extends to staff, with few black and minority ethnic staff in senior roles and many facing discrimination, abuse and racism at work.
"The government needs to take the lead in ensuring that across all schools no teacher or pupil is held back or denied the opportunity to succeed because of their colour or ethnic, cultural or religious background," she said.
