The government is being urged to make lessons on migration, belonging and empire mandatory in every secondary school in England.

The Runnymede Trust, a race equality thinktank, said last year’s Windrush scandal had exposed a “shocking lack of understanding” at government level about the winding up of the empire.

It wants to see a new approach to teaching on the subject in schools, which will ensure all pupils learn about migration and empire, and teachers are properly trained and equipped to deal with the subject effectively and sensitively.

The trust says that migration, belonging and empire can currently be taught as part of the history and English curriculum, but whether a pupil gets to study it is largely dependent on the modules, topics or texts selected by schools.

One school leader said the subject was already well covered in various parts of the curriculum, but the report pointed out academies did not have to follow the national curriculum, making it impossible to know exactly how widely it was being studied.

The report, written with the Tide migration and mobility project at the University of Liverpool, concluded: “The number of schools teaching migration, belonging and empire is unknown.” It added that just 4% of pupils taking GCSE history choose the “migration to Britain” option, which also covers the topic of the British empire.

“Migration and empire are not marginal events: they are central to our national story. As it stands the story we are telling is incomplete,” the report said.

It added that a fresh approach was required to reflect changing classroom demographics. Nearly 17% – one in six – of children aged 0-15 in England and Wales are from black and minority ethnic (BME) backgrounds, and BME young people make up more than one in four (27%) of state-funded primary and secondary school pupils.

The report called on the government to carry out research to find out exactly what was being taught in schools, and it said teachers, who may avoid topics they feel are controversial, needed more support and training.

The Department for Education said it fundamentally disagreed with “the narrow scope” of the report. “The topic of migration and the British empire are compulsory in several parts of the history and English curriculum for both primary and secondary school,” a spokesperson said.

“Our compulsory citizenship curriculum also teaches students about the United Kingdom and the Commonwealth, which is historically linked to the British empire and its diverse, national, regional, ethnic and diverse identities.”

Kimberly McIntosh, Runnymede’s senior policy officer and one of the report’s authors, said: “The influence of migration and empire both to our history and to the richness of British culture is unmistakable. Yet whether students get taught this vital part of our national story is a lottery.

“A lack of understanding of migration and empire has consequences for contemporary Britain. Last year’s Windrush scandal laid bare the shocking lack of understanding successive governments had about the ‘winding up’ of the empire – with lives ruined as a result.

“As we grapple with our post-Brexit future, a realistic appraisal of our past and present relationships with the wider world, as well as migration and empire, has never been more urgent.”

For schools, however, there are already huge pressures on timetables. Geoff Barton, general secretary of the Association of School and College Leaders, said: “The teaching of migration is clearly an important part of learning about the society in which we live, and is already referenced in various parts of the curriculum.

“But there are only so many hours in the school day and making subjects mandatory means something else has to be taken out of the timetable. There is enormous pressure on school timetables, and school leaders are best placed to make decisions about how best to balance the competing demands.”

The historian and broadcaster David Olusoga said: “It is the story of the empire that makes sense of the Britain we live in today. If you skip over that history what you lose are the backstories of millions of British people whose ancestors came from Africa, Asia and the West Indies.

“I find it hard to believe that the Windrush scandal could have been possible if we were a country that was aware of and educated in the history of empire, decolonisation and migration after 1945.”

Dawn Butler, who is the shadow women and equalities secretary, will chair a panel discussion on the subject in parliament on Thursday. The Labour MP said: “This report contains some important recommendations and I strongly support all efforts to educate our young people on how migration and empire have shaped Britain. Currently, children only study a small section of history and it is often a biased perspective.”