The incident started in Old Road Gill last week.
But since then the problem has worsened, residents said.
Pictures of the devastation have been posted on the Facebook group, Save Old Roar Gill, which has more than 330 members.
Hastings Borough Council has also posted an update, which has been shared on the group.
Valerie Myers, from the group Save Old Roar Gill, said: “The landslip in Old Roar Gill started a week ago and has continued to take out one side of the bank at the top of the Gill, near the Old Roar waterfall.
“It has had a gradually more terrifying impact and people who live at the bottom of Penhurst Close have now been asked to leave their homes because of it.”
In its update, which has been shared on the Facebook group, the council said: “Following on from last week’s updates on the landslip at Old Roar Gill, letters have been hand delivered to residents affected in Foxcote and Penhurst Close updating on the latest situation.
“We have now received a preliminary geological survey that has identified that the slippage occurred from the land above the Gill outside of the land in the council's ownership.
“The initial slope stability exercise has identified that the slip circles appear to be very close to the nearest house foundation. The dimensions do vary between the properties. These results would however need to be corroborated by a geotechnical engineer following a ground investigation.
“As this is not council-owned land, the council cannot act further in this matter. We have advised the residents that it is the responsibility of the landowner to inform their insurance company of this potential risk to the house foundations and request that they attend urgently to carry out further investigations.
“In line with our duties under the Housing Act 2004, we must also assess whether the properties are safe to occupy until further the investigations are carried out by the insurance companies. This may result in a prohibition order being imposed, until the risk to persons can be mitigated or further information becomes available to confirm the properties are safe to occupy.
“In these circumstances, residents would have to find alternative accommodation until the property is safe for the order to be lifted. If residents are unable to find alternative accommodation, the council will seek to provide this.”