The government has turned down calls for a full public inquiry into the Yarl's Wood fire.
The blaze destroyed half the centre
Prisons minister Beverley Hughes, replying to a call for an inquiry by North East Bedfordshire MP Alistair Burt, said the present non-public inquiry would be faster at getting to the truth.
Mr Burt has also called for Group 4 and other companies involved in the detention centre fire to be forced to open their books.
Ms Hughes told the House of Commons that the undamaged parts of Yarl's Wood would begin to reopen on 28 September, housing 60 single women.
By spring 2005 up to 400 women and families will be there - 15 more than at the time of the fire.
She added that she backed the decision to set up an inquiry under Stephen Shaw, the independent Prisons and Probation Ombudsman.