Mast operators, Arqiva, said some TV and radio services have now been restored for hundreds of thousands of people, but that the task to restore all services is "a complex one".
A spokesperson said: "We are assessing all options open to us but the process is a gradual one.
"We apologise for the inconvenience but ask that you bear with us as our teams work hard to deliver solutions for as many people as possible as quickly and safely as we can."
There is continued disruption to services in North-East England due to the fire. Arqiva said Freeview estimate up to 500,000 households could be affected.
Scarborough and Whitby 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.
In its latest update, North Yorkshire Fire and Rescue Service said a 300-metre 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."
When the site is safe, the fire service will return for a closer examination.
The 314-metre structure is among the most powerful transmitters in the UK and was built in 1969 to bring colour television to Teesside for the first time.
The coverage area encompasses Harrogate, York, Filey, Whitby, Middlesbrough, Stockton, Darlington, Bishop Auckland, Hartlepool and Barnard Castle.