Flat 34 was a flat in the Park Hill council estate in Sheffield.
It was home to the Khan family: Hakim, Najia, Yaz and Sonya.
It was two doors down from Flat 27, where Anna lived.
In 2018, Hakim kept toxic waste piled up in the living room without a clue what it contained, trying to prove a conspiracy around the time of the giant spider outbreak in Sheffield.
After returning from her unwilling adventures in the Doctor's TARDIS, Yaz invited the Thirteenth Doctor, Ryan Sinclair and Graham O'Brien to tea at Flat 34, which the former two accepted. Hakim made pakora for dinner, but he and Sonya expressed frustration at no-one else being there once Yaz left to pick up Najia from work and the Doctor and Ryan left to investigate the giant spiders at Jack Robertson's luxury hotel. (TV: Arachnids in the UK)
Najia's mother Umbreen celebrated her birthday at Flat 34. She gave various presents in return to her daughter and granddaughters, including giving the watch she received from her first wedding to Yaz. She reminisced about her youth though refused to elaborate on much of it. This sparked Yaz's interest in her grandmother's personal history.
When Yaz returned home from visiting Umbreen in 1947 Punjab, she met her grandmother in the flat again. Umbreen offered to tell Yaz the story of the watch this time, but she declined, having already witnessed the events first-hand. (TV: Demons of the Punjab)