A container being taken by road from Yorkshire to the Sellafield nuclear plant in Cumbria leaked radioactive material for 130 miles, a court heard.
The cargo was being transported to Sellafield in Cumbria
Leeds Crown Court was told that it was "pure good fortune" no-one was dangerously contaminated in the incident in March 2002.
AEA Technology was transporting part of scrapped cancer treatment equipment. It admitted health and safety breaches.
The company is due to be sentenced at the court on Monday.
The Oxfordshire-based company was transporting part of a piece of cancer treatment equipment, which had been decommissioned at Cookridge Hospital in Leeds, to the Sellafield complex on 11 March, 2002.
But a "plug" was left off a specially built 2.5 tonne container to carry the contaminated material on a lorry.
Mark Harris, prosecuting for the Health and Safety Executive, said: "Through pure good fortune no-one involved in the removal, containment and transfer of the source may have been directly exposed to the radiation beam.
"The risk of such exposure was undoubtedly present - at Cookridge, during the journey and at Sellafield."
He said detected radiation at Sellafield was between 100 to 1,000 times above what would normally be considered a very high dose rate.
Mr Harris said it was beyond the capabilities of normal hand-held monitoring equipment.
He said the radiation leak took the form of a narrow "beam", which was fortunately directed vertically into the ground.
Mr Harris said the result would have been much worse if the beam had escaped horizontally.
AEA Technology - which is a privatised arm of the UK Atomic Energy Authority - admitted a series of breaches of Health and Safety regulations.
The HSE has already asked for costs of £151,323.