29th century

In the 29th century, solar flares "roasted" Earth and humanity fled on spaceships until the sun stabilised. The UK populace (ruled by Liz Ten) fled on Starship UK with the help of the last star whale. (TV: The Beast Below)
The standard of craftsmanship in the century may have been very high, as the Fourth Doctor later estimated that the interior of the Nerva Beacon had originally been built in the late 29th or early 30th century. It had been left mostly alone for at least ten thousand years. (TV: The Ark in Space)
By the 29th century, Kaldor, despite having been a human colony and knowing of other worlds, had isolated itself from other planets. (AUDIO: Occam's Razor)
A spaceship with a complement of robot drones, observed by the Twelfth Doctor to have originated from the 29th century, crash landed on Earth in the past while on a destination to the Promised Land. The ship later surfaced as the castle of Nottingham in England in 1190. By this point, the robots, masquerading as medieval knights, served the Sheriff of Nottingham, converted into a cyborg and aspiring to take the English throne. (TV: Robot of Sherwood)
The First Doctor had a golden 29th century dress in the TARDIS wardrobe. (AUDIO: Rise and Fall)
The Sixth Doctor had an appointment in the Horsehead Nebula in this century. (AUDIO: The Hourglass Killers)
The ancient Kepzyrs built temples on Kepzyr in the 29th century. (PROSE: Frank Reade, Jr.'s Electric Time Canoe)
Voga, the final moon of Jupiter, was discovered by humans in this century. (PROSE: Time Traveller's Diary)
The Thain museum stored relics from the 29th century, including a series of heat guns. (COMIC: The Klepton Parasites)
The Twelfth Doctor ended up in 1855 Crimea after making a wrong turn somewhere around the 29th century. (AUDIO: The Charge of the Night Brigade)