The spread of communicable diseases among vulnerable groups and problems with mental health care provision are likely to increase in the event of a no-deal Brexit, according to a group of public health academics.

They criticise the government’s secretive approach on post-Brexit health, saying at least 26 non-disclosure agreements have been imposed on advisers.

“The government’s claims that it is prepared for no deal are implausible and at best [its preparations] might mitigate some of the worst consequences,” they say in a paper published in the British Medical Journal.

They say no deal would be likely to increase the difficulties for people already facing poverty, poor housing options and underfunded local services.

In the event of a post-Brexit recession, they say, “likely consequences include rises in suicides, alcohol-related deaths and some communicable diseases, such as tuberculosis and HIV, especially among vulnerable groups”.

The paper’s authors include Martin McKee, a professor of European public health at the London School of Hygiene and Tropical Medicine (LSHTM); Tim Lang, a professor of food policy and consultant to the World Health Organization; and Maggie Rae, the president of the Faculty of Public Health, an association representing 4,000 public health professionals.

The paper says a no-deal Brexit would risk exacerbating health challenges and affecting life expectancy in some areas, and there is potential for medicine and food shortages as well as compromised supply chains, governance and funding.

The authors say they found no evidence in their research that the government had done a proper impact assessment on no deal and health, and they call for an urgent independent review.

The paper attempts to identify risks other than those already widely reported such as shortages of medicines such as cancer drugs.

Meanwhile, 11 organisations including the British Medical Association and the Royal College of Nursing have said no deal could disrupt the supply of medicines to the country for up to six months.

“Many medicines, including life-saving agents for cancer diagnosis and therapy, cannot be stockpiled, and for those that can, stockpiles could run out,” they said.

A spokesperson for the Department of Health and Social Care said: “As part of a responsible government, the department is doing everything appropriate to prepare for Brexit.

“The public health system will continue to work 24/7 to keep the country safe from infectious disease and to keep us healthy and well. Alcohol consumption is falling, we are committed to eliminating new transmissions of HIV by 2030, and our new green paper on prevention includes many other ways to improve the public’s health.

“We want to reassure patients that we should be fully prepared for leaving on 31 October, whatever the circumstances.”