Europe's flight ban is preventing some life-saving transplant tissue from reaching patients, and other operations have had to be cancelled because surgeons are stuck overseas.
Henny Braund, chief executive of the Anthony Nolan Trust, which finds matches for patients who need bone marrow transplants, said on Monday at least 16 British patients had already been affected.
They include a young girl waiting for marrow cells to get to her from Canada.
"It has been a nightmare," Braund said. "We have cells sitting in North America while patients in the UK are being kept in isolation waiting for their transplant to arrive."
Eurotransplant, which allocates donations of kidneys, hearts and other organs in Austria, Belgium, Croatia, Germany, Luxembourg, the Netherlands and Slovenia, said tissue that would normally be flown was having to be sent by road, limiting its distribution.
"The main problem is always to get the organs there on time," said spokeswoman Brigitte Lobee from the group's headquarters in the Dutch town of Leiden.
"No organs have been lost, but we are trying to figure out precisely what the effect has been on the allocation." Normally, some 20 percent of donor organs handled by Eurotransplant are sent cross-border.
Hospitals in Britain said they were cancelling some operations because surgeons were stuck in far-off places.
They include Christine MacAndie, a consultant surgeon at the Royal Alexandria Hospital in Paisley, Scotland, who is marooned in Oslo and told the BBC website she had cancelled all her clinics until Thursday. Officials for the pharmaceuticals industry, heavily reliant on air freight to ship medicines around the world, said they were monitoring the situation carefully but buffer stocks meant there should not be any immediate drug supply problems.
"We're comfortable that there is no threat to the supply of medicines to patients at this point in time," said Sarah Lindgreen, a spokeswoman for Anglo-Swedish group AstraZeneca.
The World Health Organisation warned on Friday that ash from the eruption of the Icelandic volcano could harm people with breathing problems once they fall to earth. Particles are not a threat as long as they remain in the upper atmosphere.