Rescuers were unable to reach passengers trapped inside the plane wreckage because of intense smoke and flames, witnesses said.
A Guardia Civil officer, who had been at the crash site, said: "Nothing remains that looks like a plane. It's horrific, everything's burned. It's a horror, I don't want to tell you. It's the most like hell I've ever seen."
The lead firefighter, Miguel Ángel Sánchez, said the survivors were all found outside the plane in a ravine.
His voice broke and he burst into tears as he told Spanish radio there had been no one alive inside the plane.
"It's been very hard. Emergencies of this kind leave an enormous mark on you," he said.
Alan Gemmell, who was on board a plane coming in to land as the Spanair flight took off, said that the rescuers reacted extremely quickly and in numbers.
"The problem was that after the plane crashed, the area around it was engulfed in flames. The firefighters could not get to the plane," he told the BBC. "That is why the helicopters came with their water tanks – they were putting out the fire."
Mr Gemmell, who lives near the airport, said the area beside the runway was very dry and it had been a hot day in Madrid, which had made the flames spread faster.
"From my seat I could see smoke coming up from the end of the runway. There was a small mushroom cloud, as you might expect after an explosion," he said.
"When we came in to land, the emergency services were alongside our plane. As we slowed, they overtook us and went straight to the crash scene. They were at the scene within two minutes. There must have been about 80 or 90 ambulances.
"I could see flames coming from the tail-end of the plane. It looked like the left wing was broken and the aircraft was lying on its side."
Pablo Albella, a Madrid city emergency rescue worker, was shocked after witnessing the aftermath. "The scene is devastating. The fuselage is destroyed. The plane burnt. I have seen a kilometre of charred land and few whole pieces of the fuselage."
Kelly Ramundo, a journalist with El Pais newspaper who saw the accident, said: "The plane was set to take off, it was late. On the second take-off attempt there was fire in the motor of the plane, which crashed very shortly after take-off."
Manuel Moleno, a Spanish journalist, said he heard "a big crash" and saw smoke rising from the runway and flames inside the plane.Reuse content