The flight reportedly departed around 1am on Wednesday, according to flight tracker data shared by campaign group Movement for Justice.
It has been widely reported seven people were on board the plane.
Originally the Home Office planned to deport 90 individuals.
The Jamaican government had expressed their concerns because of Covid-19 spreading.
Karen Doyle, of the campaign group Movement for Justice, worked on the cases of 30 people expected to fly and only three boarded the plane.
She told The Guardian: “When you prioritise the politics and optics of deportation over human life you are going to get gross injustice.”
Sanjay McLean had his ticket on the flight cancelled at the last minute when his solicitors secured a High Court injunction.
He moved to the UK aged 12 and his lawyers argued he has the right to British citizenship under the Windrush scheme.
“I’m not in a good place, I don’t know how to feel, round and round, I thought a weight was lifted of my shoulder, and now they’re doing this again. I’m an emotional wreck right now,” he told The Independent.
The Home Office confirmed nobody on the flight was a British citizen or member of the Windrush generation.
Home secretary Priti Patel added: “These individuals are responsible for some of most appalling crimes – rape, assault, grievous bodily harm, drug offences, and sexual assault of children. They have violated our laws and values and have left their victims living with the scars of the crimes that took place against them. The British people should be in no doubt of my determination to remove these criminals to protect both the victims of their crimes and the public.
“The government uses every means to continue to remove foreign nationals who have committed crimes against our citizens. We remove foreign criminals from the UK to different countries every week and this flight is no different.”