Bbcdoctorwho (in-universe)

Around late 2020, the Daleks took control of an account with 1600000 followers on a platform with a limit of 280 character observations. From this, they proclaimed that they had now gained control of Earth, and that the day of victory would be celebrated as Dalek Day - however, the Doctor infiltrated the account and took it back from the Daleks, who retreated and vowed to return on 1 January 2021. (AUDIO: Incoming Transmission)

Behind the scenes
@bbcdoctorwho is the official Doctor Who Twitter account. It has been used several times to host stories that directly or indirectly promote the upcoming series of Doctor Who.

Doctor Who: Flux marketing campaign
@bbcdoctorwho was involved with the promotion of Doctor Who: Flux, which was designed so that the audience were involved with the narrative of the arrival of the Flux:

On 2 October, 3 October, 4 October, 5 October, 6 October, 7 October, and on 8 October, the account posted "interruptions" - short bursts of distorted footage of the Thirteenth Doctor sending a message. Within the same day, the account posted what appeared to be a transcript of the Doctor saying "can you hear me?" Very quickly after, all of the Doctor Who social media accounts shut down (barring Tumblr, though that account had been inactive since January). In the evening of 9 October, all of the social media accounts returned, posting promo images of the new series as well as giving new details about it. Among the content was the webcast The Flux is Coming... which evidently showed that the "interruptions" where past of the webcast, in which the Doctor sent out a distress call waring of the arrival of the Flux, indirectly to the followers of the Doctor Who Twitter account.