The flight, from Las Vegas, had reportedly decalred a mid-air emergency earlier as it entered UK skies.
It had apparently made a Squawk 7700 call, which is the aviation term for general emergency.
The reports came from Twitter accounts that automatically post alerts when flights declare emergancies.
Live data on FlightRadar24 had showed the Boeing 747 jet still heading towards its destination, Heathrow.
It was scheduled to arrive at 3.30pm, having left Vegas at 9.30pm local time, but appeared to be landing early.
The jumbo jet then touched down safely at Heathrow at 2.59pm before taxiing to the gate.
A British Airways spokesman told Daily Star Online that the plane had not declared an emergency.
The comment came amid further reports that a medical incident had taken place onboard.
Airport Webcams said on Twitter: "British Airways #BA274 Las Vegas to London Heathrow (Boeing 747-400 G-CIVB in #BA100 Negus Retro special livery) just landed; declared Pan over UK due medical emergency on board (via ATC: 59yo male, high pulse, low BP)."
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