Three workers received an accidental dose of radiation during submarine maintenance work in Plymouth, a regulator's report says.
The incident took place in a storage facility at Devonport Dockyard in 2013, the Office for Nuclear Regulation (ONR) found.
An accidental tear in heavy plastic sheeting enclosing a component allowed the release of radioactivity.
The ONR said the incident was "minor" but wants improvements at the yard.
The accident occurred in the new equipment maintenance storage facility at Devonport when a large radioactive component from a submarine was being manoeuvred within an enclosure in the building.
The tear in a plastic sheet allowed the release of a small amount of radioactive particulate matter, some of which was inhaled by the three workers, the ONR said.
The standard measure of the biological effect of radiation is the sievert.
Chest monitoring showed the three men received radiation doses ranging from less than 10 to 50 microsieverts (millionths of a sievert) - significantly below the maximum daily dose permitted at Devonport Dockyard of 500 microsieverts and the statutory annual dose limit of 20 millisieverts (thousandths of a sievert), the report said.
For comparison, the radiation dose from flying in a plane at 35,000ft is five microsieverts per hour.
Both Devonport Royal Dockyard Ltd (DRDL), which operates the site, and ONR carried out internal investigations into the incident.
The ONR said the investigations identified a number of improvement which could be made, including better risk assessments and better handling of components such as the one involved in the incident.
The ONR said it was "generally satisfied" with DRDL's investigation.
It said it had decided not to take formal enforcement action against DRDL, but had written to the company to ensure that recommendations were put in place promptly.
However, John Large, an engineer and independent nuclear analyst, said any dose of radiation beyond what was planned for a procedure was a concern.
"Submarine operations are meticulously planned. Everything is taken into account, such as 'What would happen if that bolt seizes up'," he said.
"So each job is calculated with a radioactive dose. If it goes beyond that, it is quite serious."
The incident, which is believed to have occurred in the summer of 2013, has come to light following publication of an ONR quarterly site report for the dockyard.