Many of the 271 British citizens living on the volcanic island of Tristan da Cunha, in the south Atlantic, have developed severe breathing problems.
They need to ensure that their current medical supplies do not run out.
An international operation to provide help is being led by the Foreign and Commonwealth Office.
BBC world affairs correspondent Mike Wooldridge said the islanders were being affected by what appears to be an outbreak of viral-inducted asthma, which causes severe breathing problems.
Tristan da Cunha's one resident doctor, a South African, has issued an appeal for medical supplies.
The South African Marine Rescue Co-ordination Centre was alerted first and informed British coastguards.
The volcanic island has no airstrip, making getting medicines there difficult.
However, merchant ships in the area are unlikely to have the necessary drugs on board and a coastguard spokesman said there were no British military vessels nearby at present.
Viruses have swept through the island before but Michael Swales, chairman of the Tristan da Cunha association, said he could not recall medicines becoming exhausted on previous occasions.
He said there was particular concern about the health of the elderly and the very young.
Resident Rosemary Glass told BBC Radio Cornwall that the island's tiny four-bed hospital was full to overflowing last week, but some patients had since gone home leaving three people in hospital.
"It makes people chesty and it's hard for them to breathe," Mrs Glass said of the illness mainly affecting the elderly and children.
Tristan da Cunha is situated 2,800 km west of Cape Town, South Africa, and is part of a small group of islands.
It was at one time on the main trading route between Europe and the Indian Ocean, but the small community living there is now extremely isolated.
The community of 275 people describe themselves as living in the world's most isolated settlement.
The island is famous for a mass evacuation to Southampton in the 1960s after a volcano erupted.
The main island is about 38 sq miles (98 sq km) and the currency is the British pound.
-Ahhh! Sounds like maybe a type of coronavrus? - Raquel