They might as well refer to it as a private hospital. Built as a PFI and facilities provided by Interserve.
'A new 75,822 m² hospital, procured under the Private Finance Initiative in 2000, designed by Llewelyn Davies Yeang and built by a joint venture of AMEC and Balfour Beatty at a cost of £422 million, opened in 2005. In October 2006, the hospital was nominated and made the Building Design shortlist for the inaugural Carbuncle Cup, awarded to "the ugliest building in the United Kingdom completed in the last 12 months", which was ultimately awarded to Drake Circus Shopping Centre in Plymouth. Facilities management services are provided by Interserve.' https://en.wikipedia.org/wiki/University_College_Hospital
Bliar was PM 1997-2007. Q. Who opened the hospital? A. HM the Queen.