Britain has become a "live and let live" society over the last 30 years, with a striking desire for less interference in people's personal choices and sweeping changes in how the country views homosexuality, religion and almost every institution in the land, the annual British social attitudes survey shows.

The study, by NatCen Social Research, which surveys a representative sample of more than 3,000 people annually, found that the nation has changed beyond recognition in the three decades since it first began examining society, with people now much less bound by class, gender and sexuality. Researchers also noted a recent shift towards a "more sympathetic stance on welfare benefits and recipients". Some 51% of people now take the view that benefits for unemployed people are "too high and discourage work", down from 62% in 2011.

Hostility is on the rise, though, towards the banks and Europe. Euroscepticism, perhaps today's most obvious political trend, is, as the report points out, "firmly in the ascendancy, with a record 67% wanting either to leave or for Britain to remain but the EU to become less powerful".

On the issue of homosexuality, in 1983 only 41% thought it "acceptable for a homosexual person to be a teacher in a school". Nowadays, 83% think it is acceptable for a gay man or lesbian to teach in a school. During this period the age of consent has been slashed, cabinet ministers have been openly gay and same-sex marriage has been legalised.

Changes in cultural attachments have also been profound. In the early 1980s most people identified with a religion and with a political party. In 1983, around two in three people considered themselves to belong to one religion or another; in 2012, only around half do so. This social liberalism has come in the wake of a consensus around economic liberalism. The report points out that the proportion of people who believe the government has a responsibility to provide a decent standard of living for the unemployed has fallen from 81% in 1985 to 59% today. This break with collectivism appears to support the coalition's message of self-reliance.

The antipathy to public spending can also be unearthed in views to the NHS. While the public remains firmly committed to a system free at the point of use for all, NatCen says "support for increased spending on the NHS is currently lower than at other points in the last 30 years".

However, Ed Miliband can take solace from the fact that the experience of austerity and cuts to welfare appears to be changing people's minds. Commenting on the recent fall in the numbers of people who believe benefits are too high, Alison Park, the head of society and social change at NatCen, said: "The 30 years of NatCen's British social attitudes survey shows that the nation has become much more cynical about the welfare state and benefit recipients, but austerity seems to be beginning to soften the public mood. It's also clear that on some issues the public are very divided in their views."

The standing of Westminster, meanwhile, has never been lower. Only 20% trust government to put the nation's needs above those of a political party, down from 38% in 1986.

This figure comes at a time when NatCen's survey reveals a long-term upward trend in people's belief that they both understand politics and can influence government. The proportion of voters who feel they have no say in what government does fell from 71% in 1986 to 59% in 2012.

The old order of Britain, where the traditional pillars of society were respected, appears also to have been shaken by scandals that have eroded trust. Back in 1983, nine out of 10 people thought that banks were well run; but, says NatCen, "in the wake of the financial crisis of 2008, now just 19% do so".

Newspapers, racked by soul searching in recent years, have seen their stock fall too: 30 years ago, 53% of those surveyed thought they were well run. That has halved. The report warns: "Public opinion, at least partly, reflects the behaviour of the people and institutions in question – whether they be politicians, journalists or bankers. So their future public standing lies to a large extent within their own hands."

With the arrival of Prince George and the glamour of the royal wedding, it is unsurprising perhaps to find that monarchy bucks the trend. In 1983, as many as 65% said it was very important for Britain to continue to have a monarchy. By 2006 about a quarter of respondents agreed. Now that is back up to 45%.

The data also reveals moral minefields for British society. One such issue is abortion. While in 1983, just 37% endorsed what might be regarded as a woman's right to choose, this figure is now about 62%. However, the report says that "most of this shift in attitudes occurred during the 1980s. Since then public opinion has shown little sign of shifting further, and there seems little reason to presume that Britain is heading towards some new moral consensus on this issue."

Another area of heightened public policy concern is childcare. Most people, NatCen says, believe that there should be some paid parental leave when a child is born – with the majority opting for six months. Just one in ten suggest that no paid leave should be available. However there is an obvious gender divide: women tend to support one year's leave.

Education is no longer strongly linked to a person's views about premarital sex; although in the 1980s graduates were more liberal than other groups on this matter, the views of all groups defined by educational achievement have become steadily more liberal over time.

The report identifies a definable "generation game". The young are less likely to consider themselves part of any particular religion or political party, more suspicious of the benefits of welfare and less supportive of traditional family structures.