Joseph Williamson, nicknamed the Mad Mole of Edge Hill, (TV: The Vanquishers) was a philanthropist in early-19th century Liverpool. He had a mysterious awareness of the chaotic state of time and the universe in connection to the Flux crisis, and indeed, seemed capable of wandering across different times and places. The Doctor had always wanted to meet him. (TV: The Vanquishers)
While overseeing excavation on his land, he discovered an underground chamber containing various doorways to other parts of the Multiverse, as well as the future. Travelling through one of them, Williamson saw Earth being destroyed by the Flux in December 2021. Williamson resolved to save humanity from this crisis by building a network of underground tunnels, allowing people to escape via the doorways. (TV: The Vanquishers) He was criticised by his contemporaries for the seeming lack of purpose to his tunnels, of which he spoke cryptically and evasively, (TV: The Halloween Apocalypse) and was mockingly nicknamed "the mad mole".
On All Hallows' Eve 1820, interference by the Division as they attempted to destroy N-Space caused some of the gateways to change. (TV: Survivors of the Flux) As a result, Williamson found himself wandering in the corridors of the Temple of Atropos on the planet Time. There, he stumbled upon Yasmin Khan, who had been transported there after being swallowed by the Flux after it came into contact with vortex energy. The two exchanged a few words, with Yasmin informing him that from her perspective the year was much different from 1820. Williamson found this interesting, but soon wandered off, refusing to explain his presence or to let Yasmin follow him; he claimed people following him was always "to no avail", in his experience. (TV: War of the Sontarans)
Whilst in the midst of a time storm after taking the place of a broken Mouri in the Temple of Atropos, Dan Lewis found himself with Williamson in a tunnel. Williamson was using an alien weapon to shoot at an unseen assailant and helped Dan evade particles of the Time Force. (TV: Once, Upon Time)
After once again going through one of the doors, Williamson found himself on an ocean liner in 1904. He once again encountered Yasmin and Dan along with Eustacius Jericho. He complained about the "shifting doorways" and stormed out, disappearing back to 1904 Liverpool. Yasmin and the others tracked him down and told him that the Earth would soon be under attack. Williamson showed them the chamber containing the doorways, warning Jericho not to touch Doorway Nine as it contained "endless death". The four of them were then interrupted by a banging on one of the doors, heralding an attack by the Sontarans, (TV: Survivors of the Flux) which was repelled via the "rays of death" behind Doorway Nine.
When more Sontarans arrived, Williamson and the others escaped through the door leading to 2021, when the Sontarans had taken over the planet. The Thirteenth Doctor later congratulated him on his work before he returned to his time, knowing that his work was appreciated in the future. (TV: The Vanquishers)
Behind the scenes
In the real world, the tunnels' true purpose is unclear, and is the subject of much academic speculation.