Up to 350 tonnes of anatomical waste - five times more than the company's 70 tonne limit - has now been placed in fridges.
Health minister Stephen Barclay announced in Parliament today that arrangements have been made to replace services provided by Healthcare Environmental Services (HES), a company which removes waste from several hospitals in England and Scotland.
Healthcare Environmental Services (HES) has said it is working to reduce the volume of waste after reports that a huge backlog of medical and other kinds of matter had been allowed to build up.
Healthcare Environment Services (HES) had their contracts terminated by 15 Trusts on Tuesday after "failing to demonstrate that they were operating within their contractual limits".
"We are supporting the Government and the NHS to ensure there is no disruption to public services and for alternative plans to be put in place for hospitals affected to dispose of their waste safely".
'In this instance, the primary concern was that too much waste was being held in a number of waste storage and treatment sites by a contractor, Healthcare Environment Services.
Mr Barclay said the facilities management company Mitie had taken over NHS contracts after trusts formally ditched HES as their provider at 4pm on Sunday.
Last month, health and social care secretary Matt Hancock chaired a COBRA meeting and ordered £1 million to be earmarked to help up to those trusts affected.
It added that the company's sites stored clinical waste in strict accordance with EA regulations.
"Consequently, 15 NHS Trusts served termination notices to HES formally to terminate their contracts at 4pm on Sunday October 7".
"We are taking enforcement action against the operator, which includes clearance of the excess waste, and have launched a criminal investigation".
"NHS services continue to operate as normal", Mr Barclay told MPs.
The Environment Agency partially closed HES's Normanton site on October 3 following breaches of the environmental permit.