The average number of refugees arriving each day in Greece is at the highest level since May - with thousands of children at risk in congested camps, according to Save the Children.
Arrivals during the first two weeks of August were up 144% compared to the first 14 days in July - bringing the total number of refugees and migrants to more than 10,300.
More than 3,800 children are among those stranded on the islands.
While the numbers are much lower than last year, closed camps on the islands mean that families are unable to leave. Limited movement to the Greek mainland is also putting added pressure on the congested camps on the islands of Lesvos, Chios and Samos.
Children and women are having to live in demoralising and unsafe conditions, according to the charity, which has been helping refugees across Greece since August 2015.
Katie Dimmer, Save the Children's director of operations in Greece, said that the situation was almost "back to square one".
"As the number of arrivals creeps up again, we're starting to see scenes reminiscent of last summer. Except this time, most asylum seekers are unable to continue their journeys, and are trapped on the islands, in overcrowded facilities, and under the blazing sun.
"Mothers with small babies are being forced to sleep on the ground in make-shift tents, children and breastfeeding women are suffering from dehydration due to water shortages in some camps, and tensions are increasing as basic services, such as toilets and showers, are stretched.
"Families who have fled violence and death in their homeland continue to live in fear and do not feel safe. They have told Save the Children staff that they are too scared to let their children out of their sight due to the frequent protests and a lack of security in the camps."
Save the Children is calling on the EU to provide more resources to Greece so that facilities can be improved.
Ms Dimmer said: "It's absolutely disgraceful that refugees and migrants have been living in dirty, unsafe conditions for more than four months with no end in sight.
"The EU must immediately provide more resources to Greece to improve accommodation facilities, and speed up the processing of asylum claims and the relocation and family reunification programmes."
Liberal Democrat leader Tim Farron said: "Only 20 of the 88,000 unaccompanied child refugees in Europe have been allowed into the UK. And of 40 kids from camps in Calais who have so far been allowed to join their family here, all needed a legal challenge by UK citizens or charities against their own government.
"This is a stain on the conscience of Theresa May and it is a stain on Britain's reputation.
"We also have problems on our doorstep. A meeting of British and French officials to sort out Calais is long overdue; they must establish a concrete plan of action rather than simply offer warm words over the next few days."
He added: "It is a failure of the French and UK authorities that as many as 600 children are living in the camp, and those with links to the UK must urgently be reunited with their family here and offered the safety, security and support that they have so far been denied."