The UK "no longer" has a system rigged against people from ethnic minorities, a review set up by No 10 says.
The Commission on Race and Ethnic Disparities said family structure and social class had a bigger impact than race on how people's lives turned out.
It said children belonging to ethnic minorities did as well or better than white pupils, but overt racism remained, particularly online.
The Runnymede Trust think tank said it felt "let down" by the report.
The commission was set up after Black Lives Matter anti-racism protests across the country last summer - triggered by the killing of George Floyd in the US.
The main findings were:
- Children from ethnic-minority communities did as well or better than white pupils in compulsory education, with black Caribbean pupils the only group to perform less well
- This success in education has "transformed British society over the last 50 years into one offering far greater opportunities for all"
- The pay gap between all ethnic minorities and the white majority population had shrunk to 2.3% overall and was barely significant for employees under 30
- Diversity has increased in professions such as law and medicine
- But some communities continue to be "haunted" by historic racism, which is creating "deep mistrust" and could be a barrier to success
The commission's report concluded that the UK is not yet a "post-racial country" - but its success in removing race-based disparity in education and, to a lesser extent, the economy, "should be regarded as a model for other white-majority countries".
A foreword to the report by chairman Tony Sewell, an education consultant and ex-charity boss, said: "We no longer see a Britain where the system is deliberately rigged against ethnic minorities."
While the "impediments and disparities do exist", it continued, they were "varied and ironically very few of them are directly to do with racism".
The report added that evidence had found that factors such as geography, family influence, socio-economic background, culture and religion had "more significant impact on life chances than the existence of racism".
"That said, we take the reality of racism seriously and we do not deny that it is a real force in the UK."
The report also said there is an "increasingly strident form of anti-racism thinking that seeks to explain all minority disadvantage through the prism of white discrimination" which it said diverted attention from "the other reasons for minority success and failure".
In a statement issued after the report was published, Prime Minister Boris Johnson said it was "right" that ministers now consider its recommendations in detail and assess "the implications for future government policy".
He added: "The entirety of government remains fully committed to building a fairer Britain and taking the action needed to address disparities wherever they exist."
Speaking on BBC Radio 4's Today programme, Dr Sewell said while there was anecdotal evidence of racism, there was no proof that there was "institutional racism" in Britain.
"No-one denies and no-one is saying racism doesn't exist", he said.
"We found anecdotal evidence of this. However, evidence of actual institutional racism? No, that wasn't there, we didn't find that."
Dr Sewell added that the term "institutional racism" is "sometimes wrongly applied" as a "sort of a catch-all phrase for micro-aggressions or acts of racial abuse".
Prof Kehinde Andrews, a professor of Black Studies at Birmingham City University, said the report was not a "genuine effort to understand racism in Britain".
Prof Andrews said: "It's complete nonsense. It goes in the face of all the actual existing evidence. This is not a genuine effort to understand racism in Britain. This is a PR move to pretend the problem doesn't exist."
Baroness Kishwer Falkner, chair of the Equality and Human Rights Commission, said: "This report rightly identifies the varied causes of disparities and by making recommendations to address them gives the government the opportunity to design policy targeting the sources of inequality.
"There are a number of recommendations we can play a leading role in and we welcome the recognition that additional funding would help us carry out our important work to tackle discrimination and disadvantage."
Dr Halima Begum, chief executive of the Runnymede Trust, a race equality think tank, said she felt "deeply, massively let down" by the report, and that the government did not have the confidence of black and minority ethnic communities.
Asked for her view on the commission's suggestion that the UK is not institutionally racist, she said: "Tell that to the black young mother who is four times more likely to die in childbirth than her young white neighbour, tell that to the 60% of NHS doctors and nurses who died from Covid and were black and ethnic minority workers.
"You can't tell them that, because they are dead.
"Institutionally, we are still racist, and for a government-appointed commission to look into (institutional) racism, to deny its existence is deeply, deeply worrying."
She added: "We feel that if the best this government can do is come up with a style guide on BAME terminology, or what we should do about unconscious bias training, or extend a few school hours, then I'm afraid this government doesn't carry the confidence of black and ethnic minority communities any longer, certainly not on race."
Dr Begum also claimed the report had failed to acknowledge the "suffering" of black and ethnic minority communities, adding: "All this is is a whitewash and a script that has been written to 10 Downing Street."
She also questioned the suitability of Dr Sewell and head of the Number 10 policy unit Munira Mirza, who had a role in setting the commission up - both of whom have questioned the existence of institutional racism previously.
The 258-page report makes 24 recommendations which include:
- Extended school days to be phased in, starting with disadvantaged areas, to help pupils catch up on missed learning during the pandemic
- Children from disadvantaged backgrounds should have access to better quality careers advice in schools, funded by university outreach programmes
- More research is needed to examine why pupils perform well in certain communities, so this can be replicated to help all children succeed
- The acronym BAME (Black, Asian and Minority Ethnic) should no longer be used because differences between groups are as important as what they have in common
- Organisations should stop funding unconscious bias training, with government and experts developing resources to help advance workplace equality
Frances O'Grady, general secretary of the Trades Union Congress (TUC) said the commission had "chosen to deny the experiences of black and minority ethnic workers" who were "far more likely" than white workers to be in "low-paid, insecure jobs".
She added they have been "far more likely to be exposed to Covid infection and far more likely to die - because they are far more likely to be in frontline roles.
"This is institutional racism. And it traps too many black and minority ethnic workers in poverty, insecurity and low pay."
Labour leader Sir Keir Starmer said he felt "disappointed" with what he had seen of the report's findings so far, insisting there were "structural" issues that needed to be addressed.
Speaking on a visit to Leeds, he told reporters that whilst there was "an acknowledgement of the problems, the issues, the challenges that face many black and minority ethnic communities" there was also "a reluctance to accept that that's structural".
The report had been due to be published last year but was pushed back until 2021, with the commission blaming Covid restrictions and the large number of responses from the public for the delay.
What work has already been done on racial inequality in the UK?
- The Race Disparity Audit, published by then Prime Minister Theresa May in 2017, showed inequalities between ethnicities in educational attainment, health, employment and treatment by police and the courts
- The 2017 Lammy Review found evidence of bias and discrimination against people from ethnic minority backgrounds in the justice system in England and Wales
- Also in 2017, the McGregor-Smith Review of race in the workplace found people from black and minority ethnic backgrounds were still disadvantaged at work and faced lower employment rates than their white counterparts
- An independent review of the Windrush scandal, published in March, found the Home Office showed "institutional ignorance and thoughtlessness towards the issue of race"
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