The disclosure, days before the release of the findings of the Stephen Lawrence inquiry, will provoke intense debate over Britain's future direction as a multicultural society.
The Commission for Racial Equality, which has produced the report, called for detailed government research into the nature of racist attacks on white people.
CRE chairman Sir Herman Ouseley said: "It would be irresponsible for us to not try to take this on head-on and understand it better."
He said: "It's absolutely clear in our view that you can be black and racist. Clearly the evidence we have shows that this is not just a white problem."
The CRE report, called Racial Attacks and Harassment, records that 238,000 white people told researchers they had been victims of a racial offence in a 12-month period, compared to 101,000 Asians and 42,000 blacks.
Race experts believe that many of the white victims could be Jewish, Irish or from other European minorities.
Other incidents result from tensions between the English, Welsh and Scottish, which are increasingly seen as racial.
It also believed that some white victims of crimes such as street-robberies, where a disproportionate number of offenders are black, are reporting the incidents as race attacks.
Sir Herman said that the "white" category was "very broad" and that it did not necessarily follow that a white victim had been racially abused or attacked by someone of a different skin colour.
He said: "It is easy to put interpretations which are not accurate onto figures, and at the moment the figures are a bit too bald."
The CRE report, which draws on a wide range of government and academic research studies, comes as local authorities across England and Wales are conducting audits of race attacks.
Bradford Metropolitan District Council reported last month that police records of racial attacks showed that 52 per cent of victims were white, 9 per cent black and 35 per cent Asian. Suspects were described as 50 per cent Asian, 37 per cent white, 2 per cent black and 11 per cent unknown.
The CRE report points out that, because of their smaller numbers, members of minority ethnic groups are still far more likely to be victims of racial attacks than whites.
Some 8 per cent of Pakistanis reported being victims in a year, compared to 5 per cent of Indians, 4 per cent of Caribbeans and 1 per cent of whites.
The CRE report coincides with findings published today by the Institute for Public Policy Research showing that, as Britain has become more multiracial, parts of the white population have grown defensive and insecure.
Yasmin Alibhai-Brown, author of the IPPR study, states: "Increasingly, white people of all classes are feeling deep anxieties about the loss of white identity as we go into the next century and into further integration with Europe."
IPPR research in the inner London district of Somers Town, found the five most common words used by whites to describe neighbouring Asians were "scroungers", "dirty", "animals", "pigs", and "not British".
In response to such attitudes, eight young Asian men told the IPPR that they "would retaliate with physical force if they were provoked" and that they "hated these whites". Five said they had attacked white boys and would do so again.
Even in the more affluent London borough of Richmond and Hounslow, researchers found that "some black and Asian families had developed a hatred for white people".
Partly as a result of this, some whites now say they have been victims of racial offences.
But other white victims will be Irish, Jewish, gypsies and travellers, English settlers in Scotland, and Scottish settlers in England. Dane Kim Stevns-borg came to live in England because he was so impressed by the hospitality he received as a visiting football supporter during the Euro 96 tournament.
But in October he took his Sheffield employer to court for racial discrimination after his supervisor repeatedly referred to him as a "Danish bastard".
A report next week by the Refugee Council will show that the latest people to be targeted by racists in Britain are newly-arrived Kosovan refugees.
Rachel Rees, of the Refugee Council, said many Kosovans in Dover are too frightened to speak publicly in their native language in case they are attacked by racists. One elderly couple were forced to flee their home after a brick was thrown through their window.
Meanwhile the IPPR study reveals evidence of discord between some members of different Asian communities.
The research indicates that Britain is following America's path towards a more segmented society. Ms Alibhai-Brown said years of government inaction had inhibited integration and called for a national strategy of multiculturalism to bring the British public closer together.
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