A petition to save the BBC red button will be handed in to the BBC and Downing Street on Monday, signed by more than 100 organisations.
The text part of the service will close over the next few weeks, with the first changes happening in the coming days.
The petition has been organised by the National Federation of the Blind of the UK (NFBUK).
They say the red button is vital for the elderly who have limited sight and hearing and are not on the internet.
Red button text launched in 1999, taking over as Ceefax was phased out.
The decision spells the end of reading headlines, football scores, weather, travel news and more on TV sets, 45 years after the launch of Ceefax.
But the video elements - such as allowing you to watch extra courts at Wimbledon, or stages from Glastonbury - will continue.
A BBC spokesman said that "changes" to the service will begin happening from Thursday but the complete shutdown of the red button will take "a few weeks".
Analysis by David Sillito, BBC media and arts correspondent
Ten years ago, 12 million people a week used to press the red button. It was also reaching around five million people who did not have access to BBC online.
Since then, smartphone use has mushroomed - nearly 80% of adults now own one. The red button was, even in 2010, looking a bit old-fashioned and it wasn't cheap, the text and video services cost £39 million a year to run.
Maintaining and updating a service that is used by a rapidly declining audience is hard to justify at a time when the BBC is looking to make big savings.
However, for people who have no access to online services it is for some households (after the demise of other teletext services) the only way to check headlines or weather reports at the touch of a button. It is also easy to read and simple to navigate.
And while it is only the text services that are being closed down, for some it will be the loss of a service they have relied on ever since the days of Ceefax.
The BBC says independent research, conducted before the changes were announced, concluded that the vast majority of people could access red button information in alternative ways, such as TV, radio and online services.
"From early 2020, viewers will no longer be able to access text-based BBC News and BBC Sport content by pressing red," a BBC spokesperson said at the time of the announcement.
"It's always a difficult decision to reduce services, and we don't take decisions like this lightly, but we have taken it because we have to balance the resources needed to maintain and develop this service with the need to update our systems to give people even better internet-based services.
"Viewers can still access this information on the BBC website, BBC News and Sport mobile apps - as well as 24-hour news on the BBC News Channel."
The petition demands an immediate pause on the withdrawal of the BBC Red Button Teletext service which is due to be phased out from 30 January and immediate clarification and public scrutiny on how the BBC came to the decision to switch it off.
Several protesters were seen outside the BBC's New Broadcasting House in London on Monday morning ahead of the petition hand in.
The NFBUK said the service was "vital" for people who are not online "who want to find out information independently in an easy, convenient and accessible format".
It said it feared its withdrawal "will leave many people, who are already vulnerable, further isolated and marginalised from society".