29th century
From Tardis Wiki, the free Doctor Who reference
{[timeline}}In the 29th century, the Earth Empire continued to flourished.[source needed] However, solar flares 'roast' Earth and humanity flee on spaceships until the solar flares stabilise. The UK populace fled on Starship UK. (DW: The Beast Below)
The standard of craftsmanship in the century may have been very high, as The Doctor estimated that the Nerva Beacon had originaly been built in the late 29th or early 30th century. (DW: The Ark in Space)