Operator Arqiva said they had started the process to “gradually restore” services using a combination of temporary structures and existing infrastructure, but did not give a date for when that will be completed.
A 300-metre exclusion zone has been set up around the mast, near Helmsley, which transmits Freeview television and radio signals to homes across North Yorkshire, Teesside and County Durham.
Arqiva said Freeview anticipate up to 500,000 households could be affected, including around 200,000 who use Freeview as their “primary TV platform”.
Scarborough MP Robert Goodwill said people in Whitby were likely to be badly affected as the vast majority get the signal from Bilsdale.
He said: “This is particularly of concern for older people or maybe even students who haven’t got a Sky dish and rely on the signal from Bilsdale.”
Mr Goodwill, who said TVs in his house had been affected - although they did have Sky in the living room - said people needed to have a "reasonable estimate" of when it would be fixed before deciding whether to incur the expense of getting aerials retuned to the Emley Moor mast at Huddersfield.
"Certainly in the southern part of Bilsdale there's an option to push the aerial in the other direction.
"But there's no point doing that if the signal is restored in a short time.
"I know in Whitby people will almost exclusively get Bilsdale output."
Arqiva said: "We have started the process to gradually restore services using a combination of temporary structures and existing infrastructure elsewhere in the region, and will be moving through the process as quickly and safely as possible.
"We will continue to share updates as we have them."
In its latest update North Yorkshire Fire and Rescue Service said the exclusion zone will remain in place until the site operator can confirm the tower is structurally secure.
They said: "At this time there is nothing to suggest that the first is the result of any criminal activity but this cannot be confirmed until a closer examination has been carried out."