A criminal investigation has been launched after a backlog of medical waste including body parts was allowed to build up at several disposal sites.
It emerged on Thursday that the waste from hospitals had not been disposed of in a timely fashion by contractor Healthcare Environmental Services.
The Environment Agency said the firm was in breach of permits.
The Scottish Environment Protection Agency is monitoring two sites where enforcement notices have been issued.
The Department of Health in England said there was no risk to the public.
Healthcare Environmental Services has a headquarters in Shotts in North Lanarkshire.
The contractor removes the waste from a significant number, but not all, hospitals in England and Scotland.
The waste was being held at five sites in England and one in Scotland, and is stored in secure and refrigerated containers.
The problem was first reported by the Health Service Journal (HSJ), which said the disposal company was blaming the backlog on a shortage of high-temperature incinerators.
A Cobra meeting to discuss the issue was chaired by English Health Secretary Matt Hancock last month, the HSJ reported.
A spokeswoman for the Environment Agency in England said it had found Healthcare Environmental Services to be in breach of environmental permits at five sites which deal with clinical waste.
She added: “We are taking enforcement action against the operator, which includes clearance of the excess waste, and have launched a criminal investigation.
“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.”
The Scottish Environment Protection Agency (Sepa) said it was working closely with the Environment Agency and “robustly monitoring sites in Scotland”.
A spokesman added: “On 12 September Sepa issued enforcement notices to Healthcare Environmental Services regarding sites in Dundee and Shotts, with officers conducting ongoing monitoring.”
Healthcare Environmental Services has a transfer station for waste in Dundee and a storage, processing and incineration site at Shotts.
SEPA said the company had not gone over its agreed regulatory limits for either of the two Scottish sites.
A UK government spokesman said it was monitoring the situation closely and had made sure that public services – including NHS Trusts – had contingency plans in place.
He added: “There is absolutely no risk to the health of patients or the wider public.
“Our priority is to prevent disruption to the NHS and other vital public services and work is under way to ensure organisations can continue to dispose of their waste safely and efficiently.”
What is Healthcare Environmental Services?
Healthcare Environmental Services describes itself on its website as the “UK’s leading independent provider of healthcare waste management”.
Its latest company accounts show it had a turnover of just over £31m in the year to the end of April 2017.
They credited an 18% increase in sales to a new treatment plant in Newcastle.
Company directors Garry and Alison Pettigrew were paid £299,521 between them.
They also shared dividends of £480,000.
The company owns land and buildings worth £3.7m.
The Scottish government said there had been no reports of any impact on these services from NHS boards in Scotland.
A spokesman added: “In the event of any disruption to service at NHS sites across Scotland, NHS Scotland already has contingency plans ready to put into place to ensure there is no impact on services to patients or staff.”
Healthcare Environmental Services said it had highlighted the reduction in the UK’s high-temperature incineration capacity for the last few years.
A spokesman added: “This is down to the ageing infrastructure, prolonged breakdowns and the reliance on zero waste to landfill policies, taking up the limited high-temperature incineration capacity in the market.
“Over the last year, this reduced incineration capacity has been evident across all of the industry and has affected all companies.”
At one site in Normanton, West Yorkshire, excess waste levels reached 350 tonnes in September, the HSJ reported.
This is five times more than the company’s 70 tonne limit.
Jonathan Ashworth, Labour’s shadow health and social care secretary in England, called on Matt Hancock to make a statement in the House of Commons on the “staggering revelations” next week.
“When something of this scale is going on which the government has known about for some time they have a responsibility to come to parliament and explain to parliament whether they’ve got credible contingency plans and to reassure MPs who will represent those 50 hospital trusts,” he told BBC Radio 4’s World At One.
“Given the scale of this, it’s hugely disappointing that the secretary of state has not done this,” he added.
Unison’s head of health, Sara Gorton, described the situation as “simply horrific”, saying it was “unlikely that such a distressing situation would have happened had the service remained in-house”.
Please include a contact number if you are willing to speak to a BBC journalist. You can also contact us in the following ways: