Conspiracy theorist Clive Finch kept materials relating to the Doctor in his shed, which he shown to Rose Tyler. (TV: Rose) Clive's shed was mentioned in a tribute on his website (PROSE: Dummy Massacre) after his death. (TV: Rose, etc.)
The Unbound Doctor adored sheds. (AUDIO: Asking for a Friend)
Upon first seeing the Fifteenth Doctor's TARDIS, the bounty hunter Rogue dismissed it as a "shed." The Doctor protested that it was his ship, to which Rogue asked who would travel in a shed incredulously. Later, when the Doctor asked Rogue if he was ready to enter the TARDIS, he told him it wasn't his first shed. (TV: Rogue [+]Kate Herron and Briony Redman, Doctor Who series 14 (BBC One and Disney+, 2024).)