Police were greatly outnumbered and stood back as Buddhist mobs, including monks, smashed and ransacked shops apparently owned by Muslims, the video's voice-over said.
The violence and beatings took place March 20-21 in the central Myanmar town of Meiktila.
"The police watch, hopelessly outnumbered, as the shop is torn apart," the narrator says.
A motorcycle taxi driver claims Muslims dragged off his Buddhist monk passenger off the bike and then killed him.
Other footage of a different event shows a man -- "almost certainly a Muslim," the BBC announcer said -- lying on the road, his body badly burned after being set on fire by the mob.
Someone calls for water but another voice off-camera shouts: "No, no water for him -- let him die!" Meanwhile, policemen walk around the man "watching but not helping," unable or unwilling to intervene.
A more brutal slaying was captured on video in a field when what appeared to be a teenager was clubbed repeatedly by men -- one of them a monk -- with long sticks. Another man soon appeared with what seemed to be a sword, the BBC announcer said, and he delivered "what appears to be a fatal blow."
Police reinforcements eventually arrived and order was restored but not before at least 43 people died in the sectarian clashes, the BBC said.
The flashpoint was an argument in a Muslim-owned gold shop in Meiktila, followed by an attack on a Buddhist monk who died in hospital, the BBC said.
Violence spread to at least three towns where mosques and houses were reportedly set on fire.
Since then, police and security forces have helped Muslims leave areas where they feel unsafe and installed them in isolated, guarded compounds, with no knowledge on when they might return to their homes.
The release of the BBC report comes at an embarrassing time for the Myanmar government of former military dictator President Thein Sein as he courts international aid, foreign investment and the lifting of economic sanctions.
Human Rights Watch published a report Monday claiming the government is engaging in the killing and ethnic cleansing of Rohingya Muslims in Rakhine state, formerly called Arakan state.
The video and Human Rights Watch's report were published as the European Union plans to lift the last of its trade, economic and individual sanctions against Myanmar, although a weapons embargo remains.
During the 1980s, the junta declared Rohingya non-citizens, which is still their status.
Around 735,000 Rohingya live in Rakhine state's northern area, close to the Bangladeshi border, as estimated by the human rights organization Arakan Project, funded by the National Endowment for Democracy.
Rohingya are related to the Chittagonian Bengali across the border and are distinct from the majority Buddhist population of Myanmar, who are of Southeast Asian origin.
Human Rights Watch's report, "All You Can Do is Pray: Crimes Against Humanity and Ethnic Cleansing of Rohingya Muslims in Burma's Arakan State," describing the forcible removal of more than 125,000 Rohingya Muslims.
The report said Rakhine officials are responsible for the acts and that security forces have stood by or participated.
Coordinated attacks against Muslim neighborhoods began in June 2012 after sectarian violence between Buddhist Arakanese and Rohingya, the report said.
Since then the Arakanese have razed Muslim villages, killing residents and burying some in mass graves. In one instance about 70 Rohingya people were killed, including 28 children who were hacked to death, the report said.
"The Burmese government engaged in a campaign of ethnic cleansing against the Rohingya that continues today through the denial of aid and restrictions on movement," said Phil Robertson, Human Rights Watch deputy Asia director.
"The government needs to put an immediate stop to the abuses and hold the perpetrators accountable or it will be responsible for further violence against ethnic and religious minorities in the country."