In his most outspoken intervention yet on race, Mr Lammy will call for an urgent "attitudinal change" in the arts world, accusing cultural organisations of restricting ethnic minority staff to menial or back-room roles.
The minister, who is of Guyanan extraction, will also say: "If you are not part of the solution to this crisis of Britishness, you are part of the problem."
"When I meet leaders of cultural organisations I am far too often the only black person in the room," he will comment. "Where there are BME [black and minority ethnic] employees, they are still largely in front-of-house or other support functions. In senior management or the curatorial professions they are conspicuous by their absence."
Mr Lammy will praise arts organisations for making progress on improving the cultural diversity of audiences, but will say the "picture is far bleaker when we look at the complexion of the workforce of our cultural institutions".
He will call for "an attitudinal change which signifies both a serious level of commitment at the top of the organisation, and a sense of urgency to redress perceptions that our cultural organisations are still too exclusive".
His speech is likely to provoke a fierce debate about race and to infuriate some leaders of cultural organisations.
Mr Lammy will also launch a thinly coded criticism of Trevor Phillips, head of the Commission for Racial Equality, who last year was attacked by politicians and community leaders after he called for the country to abandon its drive to become more multicultural.
In a newspaper interview Mr Phillips said "multiculturalism suggests separateness" and suggested that Britain should strive to achieve a more homogeneous culture.
But, speaking at the British Museum at an event to mark Black History Month, Mr Lammy will challenge this view.
"I am very nervous at the haste with which multiculturalism is being sent to the knacker's yard, as if it had achieved nothing for this country," he will say. "It is all well and good to call for greater integration. But people from different backgrounds cannot integrate unless they have some sense of where each other is coming from, and they cannot acquire that unless they live in a society in which preparation for citizenship includes learning about the cultures and histories of others."
He will talk about his own childhood, saying there were too few black cultural role models, and those that there were were "one-dimensional stereotypes".
Mr Lammy will also pay a tribute to a friend who was killed in the 7 July Tube bombings.
"My old schoolfriend James Adams, travelling to work on the Piccadilly line, killed by a young Jamaican man, not much younger than me, driven by a hatred of this country strong enough to blow himself up: if there is a more blunt challenge to our aspirations for a vibrant, multi-ethnic Britain to which all Britons feel they belong, I have yet to hear it."
VOICES FROM THE GALLERY
Is David Lammy right? The IoS asked visitors to the National Gallery and the National Portrait Gallery.
Kirit Thakore, 39, a telephone engineer from Birmingham, said: "Although [ethnic work] is getting more prevalent, the arts are still very segregated." Saad Hannan, 21, a genetics student, agreed, but he told us: "A concerted effort is needed, especially in view of the fact that, even after being given all the right opportunities, the data shows ethnic minority groups are not reaching the finish line." American ad executive David Peake, 43, insisted that ethnic communities are "under-represented", while Lorna Seymour, 30, a stage manager, believes there is a concerted push to get more minority groups in the arts. She added: "It's difficult not to make it a conscious effort. Ideally we would not have to, but something has to be done to get the ball rolling."
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