The risk of accidents and radioactive leaks from Britain's ageing nuclear bombs and submarines is getting "progressively worse" because of deepening spending cutbacks, according to an internal Ministry of Defence report.

The report, which has been released under the Freedom of Information Act, reveals that the MoD is facing an increasing struggle to maintain the safety of the nation's military nuclear activities as cuts become "yet more painful". There was a "lack of adequate resource to deliver the defence nuclear programmes safely," it says.

Written by the MoD's senior nuclear safety watchdog, the report warns that the number of incidents at nuclear sites is "too high". This poses a "risk to the workforce and public safety and to the environment, in both short and medium term".

It also says that measures meant to overcome prolonged shortages of safety engineers "may be insufficient", and criticises the MoD for failing to allocate funding for the decommissioning and disposal of 17 defunct nuclear submarines now laid up at Devonport in Plymouth and Rosyth in Fife.

The report covers 2010 and was written by Howard Mathers, the chairman of the MoD's defence nuclear environment and safety board.

It offers an assurance that levels of nuclear safety are currently "acceptable". But he adds: "My confidence in making this judgement is reduced from 2009 due to the adverse trend in resources (which I expect will become yet more painful), further aggravated by constraints on regulatory capacity."

The defence nuclear programmes are unlikely to be exempt from the pressures caused by the MoD's plan to shed 17,000 military and 25,000 civilian jobs, the report says. The aspiration for a 25% cut in operating costs "is obviously pulling in an opposite direction to the current shortfall in resource".

The study urges nuclear managers "to establish the most robust baselines possible and defend them rigorously." He cautions that the government's decision to extend the life of the existing Trident weapons system to save money "will present safety justification challenges".

The release of the 2010 nuclear safety report follows the release of reports for previous years in January.

"This again shows that the ever continuing reduction in resources is putting the safety of MoD staff and the public at increasing and indeed unacceptable risk," said Fred Dawson, a former senior MoD safety official.

"The MOD has failed to allocate sufficient resources to nuclear safety," he told the Guardian. "The report acknowledges this situation is becoming worse and not better."

Dawson worked for the MoD for 31 years and was head of the radiation protection policy team before retiring in 2009. The repeated warnings by Mathers and his predecessors were clearly failing to persuade ministers to devote enough money to nuclear safety, he argued.

John Ainslie, the co-ordinator of the Scottish Campaign for Nuclear Disarmament, accused the government of "cutting corners" on nuclear safety.

"The defence minister, Liam Fox, is determined to replace Trident, but he doesn't want to spend money on protecting the public from a nuclear accident."

The MoD stressed that it maintained the highest standards of nuclear safety and had an excellent record over the last 50 years.

"This is recognised in the report, which describes a wide range of actions we have already taken to ensure we have sufficient numbers of qualified and experienced personnel," said an MoD spokeswoman.

"As is routine for all MoD programmes, the submarine dismantling project is funded in stages and is fully funded for the current assessment phase."