The man, believed to be from the Bristol area, in the southwest of England, had been detained at Villawood since mid-November for breaching his visa conditions.
Refugee advocates say he took his own life.
His death has prompted calls for a national inquiry into the facility.
He was found not breathing in his maximum-security compound at about 3.20am (AEDT) on Wednesday, a spokesman for the Department of Immigration and Citizenship (DIAC) said.
The detainee could not be revived by paramedics and was pronounced dead at the scene.
The Refugee Action Coalition’s Ian Rintoul said it was believed he had died in the maximum security stage one area of the centre.
"This is the third death in three months at Villawood," he said in a statement."What on earth is someone being held for alleged violation of their student visa doing in the toxic environment of stage one?"
The man, who was understood to be wanted in the UK on serious criminal charges, was due to be deported.
A British Foreign Office spokesman confirmed they had been in contact with immigration authorities over the death.
"Next of kin have been informed and we stand ready to provide consular assistance to them," he said on Wednesday night.
Mr Rintoul said he received a text message from another detainee saying the man took his life in a bathroom, although the immigration department refused to speculate, saying the death was a matter for coronial investigation.
Deaths in custody have plagued the controversial facility since September, with two apparent suicides sparking week-long protests and hunger strikes.
Fijian man Josefa Rauluni, 36, threw himself off a building at Villawood on September 20, just hours before he was due to be flown home.
Iraqi man Ahmad Al Eqabi was found dead in his shower on November 16.
Mr Rintoul said the incidents showed the need for urgent reform of the mandatory detention system in Australia.
"The government’s addiction to such an authoritarian and punitive detention regime is literally costing people’s lives," he said.
"How many more lives will it take before the government puts a stop to it?"
Readers seeking support and information about suicide prevention can contact Samaritans.