In a scathing report on the centre, Professor Triggs has found that the overcrowding has led to people being housed in tents, and having limited access to facilities and services, including education for children and excursions out of the camp.

Professor Triggs, who visited the camp in October, said 1989 people were staying in four detention facilities on the island – 229 more than the "contingency capacity", and 1039 more than the operation capacity of 950.

"The Commission acknowledges that DIAC is working within considerable infrastructure constraints on Christmas Island," Professor Triggs wrote in the report released on Thursday.

"However, in the Commission's view, the fact that suitable infrastructure is not available on Christmas Island is one reason why people should not be detained on the island."

She said overcrowding had forced staff to put bunk beds in rooms formerly used for education and recreation, as well as in tents, and there had been a "significant" increase in demand for mental health services, which may not be met.

She was scathing about the detention of children, writing: "the Commission holds serious concerns about whether it could ever be in an unaccompanied minor's best interests to be transferred to a third country for processing of his or her protection claims".

She said the immigration department's description of three facilities used to house children as "alternative places of detention" was misleading because none were appropriate for children. Conditions in two of the facilities were "particularly harsh".

Professor Triggs called on the government to end mandatory detention, saying people should be detained only on a case-by-case basis that took individual circumstances into account, and the decision to detain people should be reviewable before the courts.

The Department of Immigration, which published a response to the report on its website on Thursday, said people were being housed in marquees on a temporary basis when people arrived and were separated for processing. It said authorities tried to limit detainees' stays in the marquees to between 48 and 72 hours.

It said the government "is committed" to giving children in immigration detention facilities access to education "in line with community standards and jurisdictional requirements".

But it acknowledged that children were missing out on school on the island.

"Following initial health checks and immunisations, school-age children are enrolled in the Christmas Island District School, subject to availability of school resources and the period of time they are expected to be accommodated on Christmas Island," it said. "The unprecedented number of arrivals this year has increased pressure on the availability of these resources."

The department was working with the local school and Serco to try to arrange summer school classes for detainees, but there might still not be enough time to offer education to all children. In that case, the department said, Serco – the detention centre operator – would be expected to provide programs within the centre.

The department did not directly address the issue of mandatory detention or review before the courts.