Tom Kemp, a spokesman for the organisation, told the PA news agency that they were left “on the street near the airport” because there was no one to receive them when they landed.
He said: “They are very confused about what is happening to them and distressed about it.”
Kemp said the asylum seekers have now been picked up by local welfare groups.
He continued: “When the Home Office say they’re deporting people to functioning asylum systems in Europe, they’re really saying they’ll abandon people on the streets of Madrid.
“UK and EU governments are playing games with the lives of refugees. And mutual aid groups are struggling to pick up the pieces.”
The home secretary came under fire on Twitter after announcing the deportations, writing: “Today we removed people who came here via small boat.
“They had previously claimed asylum elsewhere and had no legal right to be in the UK.
“Removals continue to be frustrated by activist lawyers, but I will not let up until this route is unviable.”