Although a no-deal Brexit was the worst scenario, even a negotiated divorce from the European Union would also damage the National Health Service (NHS), the experts said in a review published in The Lancet journal.
Britain is scheduled to leave the bloc on March 29th, and Prime Minister Theresa May has yet to secure parliament's backing for her negotiated EU withdrawal agreement.
The Lancet review, led by three UK health policy specialists, found that even under this deal or potential variations of it before the deadline, Brexit's health impact would be only slightly less harmful than in a no-deal scenario.
"Some people will dismiss our analysis as 'Project Fear'. But with just over a month to go to Brexit ... it just isn't good enough to keep saying that 'something will work out' without any details of exactly how," said Martin McKee, a professor at London School of Hygiene & Tropical Medicine who co-led the review.
The analysis used available legal and political texts on four Brexit scenarios to assess likely impact on the state-funded NHS, a much-cherished though increasingly strained pillar of Britain's welfare services.
It found that one major problem from Brexit under all scenarios would be staff recruitment and retention - in part because few provisions have been made for immigration of health workers to the UK or for long-term recognition of professional qualifications.
It also said that "under a no-deal Brexit, the absence of a legal framework for imports and exports is expected to have an immediate and drastic effect on supply chains" for medicines, vaccines, medical devices and equipment.
Despite government assurances, the analysis said, shortages would be likely because stockpiling cannot cover more than a few weeks and some products - such as radioisotopes used in medical imaging for diagnosis - cannot be stockpiled.
The British government has asked UK drugmakers to build an additional six weeks' worth of stockpiles to prepare for any no-deal Brexit, a target the industry has said will be challenging.
The review said that as one of the largest areas of public spending, any negative impact on the economy - however short-term - would put extra pressure on health service financing.