BA took the decision to go ahead with the flight to New York after carrying out extensive checks overnight on its fleet.
"We have complete confidence in our Concorde aircraft and we believe there is no technical, safety or operational evidence to suggest that Concorde should not operate safely into the future," said BA's customer services and operations director Mike Street.
Today's flight was believed to be half full. A least one passenger opted for a subsonic flight in the wake of the crash, but many more turned down offers of a refund or alternative flights.
BA had cancelled its two evening Concorde services last night in the immediate aftermath of yesterday's crash of an Air France Concorde moments after take-off from Paris.
All 100 passengers and nine crew on board the flight were killed. The plane had been chartered by a German tour operator and was taking tourists to New York to link up with a cruise ship.
Four people on the ground were killed when the plane crashed in the grounds of a hotel in Gonesse just outside Paris.
Alice Brooking, 21, a student from Hildenborough, near Tonbridge, in Kent, managed to escape from the first floor of the hotel. She told London's Evening Standard: "I just keep saying to myself over and over again: 'I'm alive, I'm alive, I'm alive'."
Air France said today that it would not be flying its Paris-New York Concorde services, but BA confirmed that it was business as usual less than one hour before the first Concorde of the day - BA001 from Heathrow to New York - was due to leave.
Mr Street said: "BA's first concern is always safety. All our aircraft are subject to continuing and exhaustive safety checks.
"We have complete confidence in our Concorde aircraft. We cancelled last night's two services while initial information on the Air France tragedy was coming in."
Mr Street went on: "Now we have had initial information from Air France and other relevant organisations from yesterday's incident. We have carried out extensive checks overnight to our Concordes operating today - to engines, airframes, hydraulic and other systems.
"We have liaised closely with the relevant air safety authorities and the aircraft and engine manufacturers. We believe there is no technical, safety or operational evidence to suggest that Concorde should not operate safely in the future."
He said that there was "no information from Air France or the French or British airworthiness authorities which leads us to believe that we should ground BA's Concorde fleet".
Mr Street added: "Meantime, our thoughts and sympathies remain with our colleagues at Air France, and those involved in this tragedy. We have been in touch with Air France regularly since yesterday's tragedy and offered any assistance we can provide."
BA operates four Concordes a day between London and New York. The other America-bound supersonic flight leaves Heathrow at 7pm.
The two flights which depart from New York's John F. Kennedy airport take off at 8.30am and 5.25pm US time, landing in London at 5.25pm and 10.25pm British time respectively.
Speaking at Heathrow today where he was checking in for the supersonic London-New York flight with BA, Brian Pople, 60, said he was determined to fly on Concorde.
He went on: "Lightning doesn't strike twice. From what I can see on the news it was probably something that happened on the ground. There was nothing wrong with its design. They've been using them long enough. It's only happened once in 30 years."
Electrical contractor Mr Pople, from Watford in Hertfordshire, was travelling to the US with his wife Wendy for a five-day break.
But the president of US TV network CNBC told how he could not face the emotional ordeal of a flight back to New York on Concorde.
Bill Bolster, 56, who transferred to a subsonic flight, said: "This is nothing to do with anything other than an emotional response. I am going to satisfy my emotions and go on another plane.
"I have total confidence in the engineers and pilot of this Concorde but I just can't face it."
