Two runways were closed temporarily and passengers were "safely evacuated" from the plane, the BBC reported.
British Airways officials said the Airbus A319 was flying to Oslo, Norway, when it was forced to turn back because of an engine fault.
Witnesses told the BBC they saw flames and smoke coming from the engine.
The airline said the 75 passengers were safely evacuated and a "full investigation" would be conducted.
Metropolitan Police at the scene posted on Twitter, "Police at Heathrow assisted in the response to the emergency landing. It is not being treated as a terrorist incident at this time."
Rob Brownell, who said he saw the plane from a location in central London, told the BBC flames were "clearly visible."
"My initial thought was, My God this thing is going to blow up,'" Brownell said "The wings are full of fuel so I couldn't see how there could not be an explosion."