Rescue flights have started to bring holidaymakers back from Rhodes, which has been ravaged by wildfires.
Up to ten thousand British nationals are thought to be on the Greek island, and holiday firms are scrambling to get them home.
Tourists have been sleeping at the airport, makeshift rescue centres and on the street after the flames threatened holiday resorts.
Smaller evacuation orders are in place for parts of Corfu and Evia.
Both EasyJet and Jet2 are planning to send repatriation flights to Rhodes on Monday, and some Tui customers returned on three dedicated flights overnight.
Hundreds of thousands of British tourists flock to Greece every year, but have described being stuck in a nightmare.
Many had to abandon their belongings and flee on foot as fires which have already destroyed homes spread from the centre of the island towards resorts on its eastern coast.
Some have had to sleep on mattresses in emergency accommodation because hotels elsewhere on the island are full.
Speaking at Birmingham Airport after returning from Rhodes, holidaymaker James Jones told the BBC he and his family fled after hotel staff came to their room and said “get to the beach”.
They had to dump their luggage on the sand while awaiting rescue from the coastguard, he said, adding: “As you looked behind you it was coming over the mountains, the fire was just moving so fast, it was horrific.”
Mr Jones said people were using clothes as makeshift face coverings to keep out the smoke, and said he told his children to “get away from anything flammable and get on the rocks, stay near the water”.
Greece has seen searing heat in recent weeks, with temperatures exceeding 40C across the country, and fires have blazed for nearly a week in some areas.
Rhodes has been battling fires fanned by strong winds since Tuesday and roughly 19,000 people have been evacuated so far in what Greek authorities say is largest operation of its kind they have carried out.
Around 2,500 people have been evacuated on Corfu, some 1,027km (670 miles) miles away, a fire department spokesman told the AFP news agency.
Boats were used to rescue people from beaches but officials have told the BBC the situation is less serious than on Rhodes.
Fires broke out over the weekend in northern Corfu, and people were told to leave the areas of Santa, Megoula, Porta, Palia, Perithia and Sinies.
Olga Kefalo O-Gianni, the Greek tourism minister, told the BBC the situation on Corfu is “not alarming” and said tourists planning on visiting parts of Corfu or Rhodes not impacted by the wildfires should still travel.
Emergency services are also tackling fires on Evia, the second largest of the Greek islands, and some areas are being evacuated, the state news agency ANA-MPA reports.
A national holiday due to take place across Greece on Monday has been cancelled.
The UK Foreign Office issued updated travel advice for Greece on Sunday, warning “the situation can change quickly, so you should stay up to date with official advice”.
It has advised people to follow emergency service guidance and to call 112 if there is immediate danger.
A team of British diplomats and Red Cross workers have been sent to Rhodes airport to assist UK nationals.
Foreign Office minister Andrew Mitchell said between seven and ten thousand British holidaymakers are on Rhodes, and the government is regularly reviewing travel advice.
He told the Today programme there is an “inevitable degree of chaos” on the ground despite local efforts, adding that it is “too early to condemn” holidays companies for their response.
Mr Mitchell said the fires are “undoubtedly a wake-up call” on climate change, adding: “It is essential that the world combats it, and Britain is playing a leading role in doing that.”
It is unclear what started the fires but extreme temperatures and dry conditions across Greece have aided their spread.
Chariton Koutscouris, the area’s head of tourism, said arson was suspected and the fire department had been warned someone was planning on deliberately starting a fire.
He said the blazes were down to a “group of people” who “get pleasure out of this with the pain of the other people”.
Maria Feggou, of the Hellenic Red Cross, told BBC Radio 4’s Today programme that the situation on Rhodes is a “nightmare” but predicted the island will return to normality before long.
The Greek government is trying to help, she added, but said the scale of the fires means “they can not provide as much help as we would like to have, because they have to be everywhere”.
George Tsuchnikas, a British man who has a home on the island, told the same programme he has taken in families from Germany, Sweden, Norway and Ireland.
He said displaced tourists are “devastated, they are tired, they don’t know what is happening next”, adding: “Lack of communication and information is the major problem, but people are doing what they can.”
Jack Askin, who landed at East Midlands airport on a scheduled Ryanair flight returning from Rhodes, told the BBC the situation had been “scary”, adding “it was really bad – we got out on Saturday night and it was carnage at the airport”.
Connie Woods, 18, from Newry, Northern Ireland, was sheltering in a school for a second night on Sunday after being evacuated from the Pefki Island hotel.
Ms Woods said there were already hundreds staying at the crowded school, with more arriving, adding: “So many young children, families with no luggage, newborn babies. It’s awful.”
Greece’s fire service has warned the situation could worsen as further villages require evacuation.
Deputy mayor of Rhodes, Athanasios Vyrinis warned people were being forced to sleep in cardboard boxes and said there were not enough essentials.
Despite the situation on the ground, flights to the island have continued to operate, with some customers arriving late on Saturday to find their hotels already evacuated.
What are holiday companies doing to help?
- EasyJet announced it would operate two rescue flights with a total of 421 seats on Monday, and a third on Tuesday, in addition to its nine scheduled flights between Rhodes and the UK.
- Jet2 is running three repatriation flights, all due to leave tonight, which will return to Manchester, Leeds Bradford and Birmingham. All flights and holidays to Rhodes have been cancelled, but aircraft with no customers on board will be flown there in order to bring people back.
- British Airways said its flights to Rhodes were running as normal, but customers needing to return early could change their flight for free, and those not wishing to travel there in the next week from the UK could postpone their flight.
- Thomas Cook said it had cancelled some holidays to affected areas, with full refunds offered. It added some customers booked to travel to other parts on Monday and Tuesday were being contacted with the option to cancel and be refunded if they wished.
- Tui operated three “dedicated flights” back from Rhodes overnight and all flights to the island have been cancelled up to Wednesday, but customers currently in Rhodes will return on their intended flights home.