The party's shadow education secretary Tristram Hunt has also announced that Labour would scrap the free schools programme if the party wins at the next election.
Speaking at a Labour fringe event organised by Progress in Westminster on Wednesday, he said: "I can wholly understand the principle that if you have Church of England, Catholic or Jewish faith schools that you should also have other communities and different faiths with their own schooling system, on a principle of religious equality."
But he said he believed schools shouldn't be allowed to operate in a completely autonomous way, saying: "We cannot have schools as islands, either around ethnicity or religion, not cooperating or forging partnership with other schools. Our answer is making sure Ofsted inspects schools on the basis of a broad and balanced curriculum."
One of Labour's solutions to the issue is increased inspections by Ofsted. Mr Hunt said: "We have particular concerns that Ofsted is not allowed to inspect religious teaching in faith schools. That seems to me to be a slightly curious situation. It is a worrying trend in terms of cultural and ethnic identification through schooling."
"You put that against the Ted Cantle report in terms of the Northern mill towns, growing divisions in terms of ethnicity, and racial and religious segregation, particularly in our cities, and exactly what we tried to undo in terms of Northern Ireland in terms of the different schooling types there and you do have a challenge."
Shadow education secretary Tristram Hunt: