Life's winners and losers were laid bare today in an official report by the Equality and Human Rights Commission into how fair Britain has become.

The commission's first three-year review, How Fair is Britain, shows that while some inequalities remain entrenched, new challenges are emerging as the country's population becomes older and more ethnically and religiously diverse.

The study identifies "five great gateways" to opportunity – revolving around well-being, education, work, security and voice in society – where millions could benefit if barriers are lifted. These should become the basis to assess "fairness" in public policy, the commission says.

In health, the report says, the poorest can expect to live seven years less than the richest. In education, boys are falling far behind with girls outperforming them at ages 5, 16 and degree level. Students of Indian and Chinese origin are streaking ahead at school.

In criminal justice, Gypsy and traveller communities appear to be targeted – and women prisoners have become a prominent feature of Britain's jails. The ageing society means that women have a 50% chance of becoming a carer before they reach 59.

Trevor Phillips, chair of the commission, says in the 21st century there are still "gateways to opportunity that appear permanently closed, no matter how hard they try; while others seem to have been issued with an 'access all areas' pass at birth".

These distinctions are more nuanced than in the past. Race matters, but so does heritage. Ethnic differences at GCSE are narrowing, except for the top end where the two highest performing groups are students of Chinese and Indian origin.

Free school meals, given only to those on low incomes in Britain, are a strong indicator of class distinctions even at the upper levels of performance. The highest performing group in England are Chinese girls, with even those on free school meals outranking every other group's "educational development" – except better-off Chinese girls.

In employment, a quarter of men of Pakistani descent drive for a living – mostly in a taxi cab.

"There's good news for some ethnic minorities who perhaps prioritise education," said John Hills, professor of social policy at the London School of Economics, who chaired the last government's National Equality Panel report. "At the same time we are seeing a huge amount of self-employment in other groups, such as Pakistani men. There's evidence to suggest that discrimination in the recruitment process keeps them out of jobs."

Prof Hills said that the report showed "we can both be upbeat and also know how far we have to go … which is hugely important given that the equal opportunity society has been put at the heart of the [coalition] government."

The commission does say that Britain is a largely "tolerant and open-minded society", which has become more socially liberal in recent decades. Opposition to working for an ethnic minority boss and aversion to mixed-race marriages has dropped. Gone too are the stereotypical views about the roles that men and women should play in family.

The study says the biggest change has been the dramatic shift in attitudes to homosexuality. "A gap of less than 20 years separated the parliamentary debates about Section 28 [which banned councils from 'promoting' homosexuality] and civil partnership."

This is not to say that Britons are not worried by the speed and direction of change in the country. The commission says this is best exemplified by the "immigration paradox": three-quarters of Britons say that they are concerned about the scale of immigration at a national level – about the same proportion feels that immigration is not a problem for their own communities.

There is also an acceptance that however far we have travelled towards being a fairer society at ease with itself, substantial evidence shows Britons get neither equal outcomes nor equal chances.

From the cradle to the grave, race, religion, class, disability and gender can all have a bearing on a person's prospects. But explanations are never simple: the report shows that black Caribbean and Pakistani babies are twice as likely to die in their first year than white British babies – yet Bangladeshi babies survive as long as their white peers.

While disabilities often mean lower income levels and life expectancy, the commission finds that "being black and male appears to have a greater impact on levels of numeracy than being learning disabled". In terms of geography, the commission says that "one in four Welsh adults lack basic literacy skills, more than in any English region and in contrast to one in six in England overall".

The gender pay gap remains – men earn 16% more than women on average and "progress appears to be grinding to a halt". But there are significant differences among women. Those with degrees are estimated to face only a 4% loss in lifetime earnings as a result of motherhood, while mothers with no qualifications suffer a 58% loss.

Disabled groups said they were concerned how, given such degrees of disadvantage, the government could target vulnerable people with spending cuts. Richard Hawkes, chief executive of disability charity Scope, said: "If disabled people in their early 20s are twice as likely not to be in employment, education or training, then we question the wisdom of the government's plans to strip away employment support services to the tune of £4.87bn over the next five years."

One of the most shocking revelations, given the acceptance of homosexuality in adult life, was the level of homophobic bullying found in schools. The commission found that two-thirds of "lesbian, gay and transgender" secondary students report that they have been victims of often severe bullying – 17% of those bullied reported having received death threats.

"It is a very worrying statistic," said a spokesman for Stonewall, the gay and lesbian rights group. "We have seen a number of recent high-profile homophobic hate crimes, including assault, where the attackers have been schoolchildren or school leavers."

Another worrying feature of crime in Britain is the prevalence of rape – and the low rate of conviction. There has been no significant fall in the level of rape or serious sexual assault recorded in the British crime survey over the last five years. Over a quarter of all rapes reported to the police in England and Wales last year were committed against children aged under 16, while that figure rose to over half for male rapes.

The review acknowledges it is not definitive. It admits to "significant gaps in knowledge and data" about particular groups, such as transgender people.

A spokesman for the Government Equalities Office said: "When people are treated fairly, everyone in society benefits. That's why this government is committed to tackling all forms of inequality and discrimination, and we welcome the EHRC's contribution to the debate. We will be studying the review's conclusions carefully."