The Health Protection Agency is investigating several cases of Legionnaires' disease in people who have been to Corfu.
The organisation said it was aware of nine cases of the disease in people aged 39 to 79 who had travelled to different areas of the island since August.
The agency is now working with colleagues in the UK, the European Centre for Disease Prevention and Control (ECDC), and Greek public health authorities to try to find the source.
They said that although the cases had all recently travelled to Corfu, a UK source of infection could not be ruled out.
The HPA is now advising people who are going to the island to be aware of the symptoms of the disease.
Caused by the legionella bacterium, Legionnaires' disease can lead to severe pneumonia. It can survive in water, and may be spread through exposure to water droplets from cooling systems, shower heads and taps, but cannot be spread from person to person.
Symptoms start between two and 14 days after exposure, often with an initial flu-like illness leading to pneumonia.
The disease is uncommon in the UK but can lead to complications and can be fatal, so early treatment is important.
Professor Nick Phin, head of the HPA's Legionnaires' department, said: "We are concerned that UK residents travelling to Corfu should be aware of this potential risk, however we are not suggesting that people change their holiday plans.
"Legionnaires' disease is very rare and cannot be spread from person to person so the risk is low.
"We are continuing our investigations so that we can provide the best advice for travellers and minimise the risk of further cases.
"Sometimes a source for the infection is never found, because the bacteria can live in a very wide variety of types of water supply."
The HPA is also briefing GPs asking them to be alert to people returning from Corfu suffering from relevant symptoms.
Click on the image below for our rundown of the top ten Greek islands...
Top 10 Greek islands
Legionnaires' disease outbreak linked to Corfu
Why we love it: It's not packed full of tourists! Ios is as known for its camping sites and lively backpacker scene as it is for its rocky coastline- great fun for diving off. The village of Chora is a gem - a labyrinth of stairways climbing a steep hill from the port.
Why we love it: This island is just four kilometres from the Turkish coast and in antiquity was considered one of the most beautiful in the Aegean. Today, with its Genoese castle, glittering waterfront and Roman ruins, Kos Town has plenty of reasons to linger, while inland, picturesque villages dot an enchanting mountainous terrain.
Why we love it: Named after Apollo's grandson, Mykonos is one of the most hedonistic resorts in the Mediterranean, attracting top DJs and a cosmo, gay-friendly crowd. Cobbled alleys wind beneath balconies overflowing with bright flowers. In the late afternoon locals love to have enjoy a glass of Ouzo on the waterfront and watch the sun go down over the sea.
Stay: The eight-roomed Belvedere Hotel offers sophisticated five-star luxury.
Naxos is the largest of the Ciclades Islands and has some of the finest beaches, particularly at Plaka, Agia Anna and Alikos. Its capital is the picturesque, whitewashed city of Naxos, which has wonderful seafood restaurants.
Stay:The Naxos Beach 1 is only a few metres away from St George's beach and all the watersports ameneties.
Why we love it: Lesbos is known as the Emerald Island because of its wonderfully verdant landscape, dominated by olive groves and petrified sequoia forests. The poetess Sappho lived on Lesbos, and it is because of her homoerotic poetry that we get the word 'lesbian'- for this reason Lesbos is a popular destination among lesbians.
Why we love it: Rhodes is associated with the Sun God Helios and the sun does seem to shine brighter here, just off the coast of Turkey. Rhodes Town is home to the stupendous Palace of the Grand Master, a huge 14th Century fortress built by the Knights of St John, a bewildering labyrinth of medieval alleyways with some of the finest shops outside Athens and minarets dating back to Ottoman rule. On the south-east coast is Lindos- its delightful beaches and old town dominated by the towering presence of a ruined acropolis.
Stay: The Elite Suites at the Amathus Hotel are THE place to stay.
Why we love it: Santorini owes its dramatic beauty to explosive volcanic eruptions, which left a huge lagoon surrounded by 300 ft high cliffs on three sides. Many of its prettiest towns- Oia, Fira, Thera- are built on the side of this huge caldera, with sublime views. Perhaps the most spectacular of all is Imerovigli, with its blue domes and winding stairwells perched over the azure abyss.
Stay: Romantics should definitely check out the Vedema Resort - one of Sovereign's Couples Retreats.
Why we love it: Many historians claim Homer's legendary hero Odysseus was not from what is now called Ithaca, but from Kefalonia. The largest of the Ionian Islands, it's home to natural wonders such as Myrtos Beach- one of Europe's most spectacular- while at Kaminia Beach you can see an endangered species of turtle, the loggerhead. Also worth visiting are the caves at Drogarati and Melissani Lake.
Why we love it: The Mediterranean's fifth largest island is forever associated with the Knossos, the ancient Minoan palace that was home to the Minotaur- a terrifying creature who was half man-half bull. Other attractions include the beautiful Venetian port of Rethymno, the leaping gorges of Samaria and the lively ouzeri taverns of Heraklion.
Why we love it: Corfu's old town is full of bistros and tavernas dotted along the 'kantounia' (cobbled streets) leading to a lovely marina and Venetian fortress, the Palaio Frourio. Large Georgian houses of white Malta stone are a reminder of bygone British rule. Paleokastritsa is one of Greece's loveliest spots, where olive and cypress-clad mountains tumble down to cliffs, harbours and sandy beaches.
Stay: The Delfino Blu, which sits on a beautiful beach, has 12 apartments to choose from.
There are fewer better ways to spend the lazy days of late summer than hopping between some of Greece's 227 inhabited islands. From crazy Corfu to cultured Kos, there's something to please everyone.