Britain's 3.6 million lesbian, gay and bisexual people see themselves confronted by huge barriers of prejudice at every level of society, according to the first authoritative poll of their views.

The poll, commissioned by the equality charity Stonewall, which said some public bodies were too "smug" about their record on discrimination, indicates that the schoolyard is the most entrenched bastion of prejudice.

The YouGov poll of 1,658 gay adults found homophobic bullying in schools is more prevalent now than in previous decades. Around 30% of lesbian and gay people expect to encounter discrimination if they were to try to enrol a child at primary or secondary school, and 80% believe they would have difficulty if they were to apply to become a school governor.

The NHS, police and courts are doing better than the education system in combating discrimination. However, a significant minority of gay people expect to be treated less well at a GP surgery or during an emergency admission to hospital.

One in four think they will be treated less fairly by police if they become a victim of hate crime, while one in five expect to find it harder than a heterosexual person to get social housing, and nine in 10 expect barriers to becoming a foster parent.

The poll also suggested prejudice is endemic in political life, with most lesbian and gay people expecting discrimination if they seek selection by a party to run for parliament. Nearly nine in 10 think they would face such barriers from the Conservative party, 61% from the Labour party and 47% from the Liberal Democrats.

Ben Summerskill, the charity's chief executive, said: "Too many public services are a bit too smug about the progress made towards fair treatment for the lesbian and gay taxpayers who help fund them.

"Last spring we heard from a 14-year-old girl who had - incautiously - shared with a teacher at a faith school the thought that she might be gay. Subsequently the girl has been required to sit outside the changing room at the beginning and end of sports lessons while the 'normal' children get changed."

Of those polled, two-thirds of lesbian and gay people under 19 said they were bullied at school on grounds of sexuality, compared with half of those aged 35-44 and only a quarter of those over 55.

Stonewall said the problem was exacerbated in schools when teachers were banned by Section 28 of the 1988 Local Government Act from doing anything that could be perceived as promoting homosexuality. Section 28 was repealed in 2003, but the charity says the education system is years behind in its efforts to tackle prejudice.

Across Britain, one in 14 lesbian and gay people expect to be treated less well than heterosexuals when accessing healthcare. Gay women are almost twice as likely to expect discrimination on grounds of sexual orientation.

There are big regional differences in perceptions of discrimination in the NHS. In Wales, 16% thought they would get inferior treatment if they were admitted to hospital in an emergency, compared with 2% in the south-west.

Summerskill said: "The research highlights the one remaining gap at the heart of Britain's legislative equality framework. There is not yet a duty on public bodies requiring them to promote equality of service for gay people in a way that already exists for gender, ethnicity and disability. We'll now be pressing the government to honour its outstanding manifesto pledge to introduce such a duty."

Summerskill said he regarded the debate about the size of Britain's lesbian and gay population as having been settled by the Treasury's actuary department, which said it was 6%, or 3.6 million people.