A company facing a criminal investigation over a pile-up of NHS waste has claimed it repeatedly warned authorities about a lack of incinerators and disposal facilities.

Garry Pettigrew, the managing director of Healthcare Environmental Services (HES), denied claims human body parts were among items caught up in a backlog at its sites.

In his first public interview since the scandal emerged last week, he claimed the Environment Agency had privately admitted to him that the system was broken. “I know just now that waste is being stored in hospitals in shipping containers, and shipping containers are being lined with black liners to stop liquids, whatever else coming out. It’s being put into skips,” he told the BBC.

HES caused a major national incident by allowing large quantities of hazardous and non-hazardous waste from hospitals to build up at some of its disposal sites across England. It included infectious waste, dangerous medicines used in cancer treatment, needles and anatomical waste, which includes body parts.

Pettigrew said the backlog accumulated because there was not enough capacity in the incinerator his company used. “Since October 2015 we have seen a major drop in incineration capacity and over the years that has got worse and obviously on numerous occasions we have told that to our NHS customers, we have told that to our Environment Agency partners and obviously at the same time we have invested heavily to get our own infrastructure,” he said.

He told the BBC his company was dedicated and professional, adding: “Every single part that people are referring to there is dealt with securely, professionally, and any anatomical waste would be stored in fridges and at the same time prioritised for outward bound.”

On Tuesday, the health minister Stephen Barclay told MPs that more than 3.5 tonnes of human body parts were stockpiled at four sites by HES, which collected £31m last year to burn waste.

Some of the company’s contracts have been terminated after the Environment Agency said on 5 October that HES had breached permits at four of its six sites and a criminal investigation had been launched.

As part of its enforcement activity, the agency partially suspended the company’s permit at one of its sites, preventing it from accepting incinerator-only waste.

However, HES continues to collect waste for more than 30 English hospitals and also carries out work across Scotland.

The Scottish Environment Protection Agency (Sepa) said it had issued enforcement notices at sites in Dundee and Shotts last month, where its officers were conducting “ongoing monitoring”.

An Environment Agency spokesperson said: “It’s not true to say there is insufficient incinerator capacity – there is industry-wide agreement that there is enough capacity to deal with clinical waste and our site inspections show the rest of the sector is performing well. However, Healthcare Environmental Services has significantly and repeatedly breached its environmental permits by storing excess waste at a number of its sites.

“We have taken a range of action with the company but they have continued to operate unlawfully. As a result, in addition to our enforcement activity to clear the sites, we have launched a criminal investigation.”