Donna Noble, desiring to go shopping, once asked the Tenth Doctor if the TARDIS had broadband. (COMIC: The Greatest Mall in the Universe)
When investigating the Zygon plot to use stasis cubes to invade a more technologically developed Earth, the Tenth Doctor commented to Clara Oswald that Zygons would never invade a place that didn't have decent broadband. (PROSE: The Day of the Doctor)
Later on, the TARDIS did indeed have broadband. The Twelfth Doctor told this to Bill Potts, telling her to watch some movies or something to pass the time while he was gone to blow up the colony planet. (TV: Smile)
The broadband in Stegmoor was very poor according to Matilda Gregson and Lilly. (AUDIO: Beachhead)
Behind the scenes[]
Broadband is a means of gaining Internet access.