Police said the attack on the 9-month-old sisters occurred when the fox entered the east London house Saturday night. London experienced unseasonably warm temperatures over the weekend.
Police described the girls' condition as serious but stable.
Neighbor Michael Parra said Monday that police had warned residents not to keep their doors open. Parra said residents "see a lot of foxes around here. They're always in our garden."
Hackney Council said it had never received a complaint about a fox attacking a human and "all the expert advice is that incidents like this are incredibly rare."
John Bryant, an expert in pest control, told the BBC that foxes tend to avoid people.
"They will walk into houses, walk round, mess on the bathroom floor and sometimes sleep on the bed if people are not around," he said, adding that he could see no reason for an attack "unless it jumped into the (crib) and then found itself with squirming children underneath it and couldn't get out.
"It just doesn't make any sense to me."