Entire villages have been destroyed in Mozambique and Zimbabwe and most of their inhabitants swept away, as rescuers race to save tens of thousands of people trapped by flood waters from Cyclone Idai.

Testimony collected from areas entirely cut off by flooding shows a situation far worse than indicated by official figures, with estimates from some witnesses suggesting that the death toll will reach the thousands.

Cyclone Idai brings devastation to Mozambique – visual guide Read more

Witnesses counted hundreds of dead bodies on one stretch of road in Mozambique and spoke of many “absolutely, totally obliterated” communities, while plantation workers in Zimbabwe said they believed 1,000 people to be beneath the rubble in one devastated village alone.

More helicopters and boats are being sent to help with the operation, and donors and humanitarian organisations have pledged support, but rescue teams are not coping with the numbers.

New satellite images of the area around the port city of Beira have revealed the vast scale of flooding. European Space Agency imagery showed a huge new inland “lake”, measuring 125km by 25km.

Play Video 1:09 Witness describes flood-hit Mozambique: 'We just saw total devastation' – audio

A businessman stranded in the flooded area after helping family and employees in Beira in the wake of the cyclone described apocalyptic scenes of death and devastation.

“Any roof that was left, and old eucalyptus plantations and any cashew tree, any tree had four, five, six, seven people in it,” Graham Taylor said. “People were trying to wade across. The more primitive type houses were totally obliterated – I think 95% of the houses were obliterated.”

Mozambique’s environment minister, Celso Correia, said 15,000 people were stranded: “They are alive, we are communicating with them, delivering food, but we need to rescue them and take them out … Our biggest fight is against the clock.”

After climbing down from the South African air force helicopter he was rescued in, José Itai said that all his relatives – his parents and three sisters – disappeared and he believed their bodies were floating in the Buzi river. He saw a woman stranded in a tree giving birth alone, and said that her baby fell into the water. “All the women who were giving birth lost babies because they had to flee,” he said.

The Guardian has heard reports of people fighting over the little food dropped by helicopters, and some falling from trees and roofs into the water and drowning.

Meanwhile, in the city of Beira, amid shortages of water, food, cash and fuel, with no electricity, and with people becoming more desperate, the situation is becoming difficult for the authorities to control.

Police fired teargas and live ammunition to disperse people trying to get into a rice-processing warehouse in the Vaz neighbourhood, home to many of the city’s food stores, on Wednesday.

Marta Mareda ran from the bullets and lost her 12-year-old daughter in the crowd. Later, she returned to where the battalion of the Special Police Unit were blocking the road, barefoot, crying and begging them to let her find her daughter. Mareda believes she may have been trampled and suffocated in the crush.

In Vaz, hungry people who had lost everything were stopping any vehicle bringing food aid through the area.

The mayor of Beira, Daviz Simango, helped clear fallen logs from roads. The main focus of the city council is currently to improve access, he said. Simango reported that 80% of the roads in the city are now passable.

'We don't have anything': the fight for survival after Cyclone Idai Read more

Simango said most of the bodies in the city morgue were from outside Beira, including those of 22 of children from neighbouring districts. The morgue roof was damaged by the storm and has been replaced by a tarpaulin, which means its refrigeration system cannot cope with the bodies constantly arriving.

“We have improvised, but the plastic does not offer any guarantee and if the electricity problem continues it will be dramatic,” Simango said.

Flights bringing food aid in from donors began arriving on Sunday, but according to officials the quantities are barely adequate to cover needs. People are rushing to withdraw money with which to buy food and survive. Without electricity, however, only one of Beira’s six banks was open, and queues of people stretched for two blocks.

The Munhava substation, the key infrastructure providing Beira’s power supply, is totally submerged and electricity supplies are not expected to be restored soon. The state-owned electricity provider EDM has sent generators to run water pumps for hospitals and other strategic services.

In 11 of Beira’s neighbourhoods the houses were reduced to rubble. One of the biggest obstacles to providing aid is the lack of access, since the floods washed six sections of the main road to Beira away. Aid agencies are now working to repair roads and bridges.

Play Video 0:23 Aerial footage shows Cyclone Idai devastation in Mozambique – video

Over the border in Zimbabwe, humanitarian workers for the International Rescue Committee estimated that 500 people in one village may have been killed by the cyclone – though the official death toll stands at 98.

Survivors in the village of Kopa in Chipinge, where there was a large banana plantation, said they believed the 1,000 bodies lay beneath the rubble of their homes.

Thokozani Copper said only three of 300 houses were still standing, and the government should work faster to save any survivors still trapped in the rubble.

“We are asking government to help us retrieve bodies so that we know how to bury them. For us, the survivors, we also need to be helped,” he said.

Additional reporting by Matias Guente in Beira and Nyasha Chingono in Chipinge, Zimbabwe