It was initially suggested Labour's equalities team might support Mr Loughton's amendment but it later put forward its own compromise proposal for an immediateconsultation.
Delta Air Lines, as well as many other carriers, contract with the University of Pittsburgh Medical Center for their STAT-MD program for immediate medical consultation when they have a problem during a flight.
"The university is pleased that the Welsh government has decided to cancel with immediate effect the statutory consultation process involving the dissolution of Cardiff Metropolitan University which we believe was legally and financially flawed, " she said.
Ms Burgess's resignation, which has taken place with immediate effect, could affect the consultation process, said Mr Green of campaign group Slough and Windsor Against The Cuts.
Labour has criticised the timing of the consultation, arguing for a more immediate "strategy" announcement, ahead of proposals for greater economic union within the eurozone being discussed at an EU summit next month.