31st century

According to Eldane, the 31st century was the time his branch of homo reptilia would awaken from the slumber into which they placed themselves in 2020. Specifically the year 3020, one thousand years after returning to their cryo-chambers. It therefore was a time of renewed contact between his species and humans. (TV: Cold Blood)

According to the Fifth Doctor, the 31st century was "all space cities and monorails." (AUDIO: The Butcher of Brisbane)

The 31st century was the start of a period of long term societal collapse for both Earth and Kustollia following "an enormous, terrible battle" between the humans of Earth and the Kustollons of Kustollia, as recalled by Igrix and the Ninth Doctor. (COMIC: The Love Invasion)

During the early 31st century, Earth Corp was testing weapons in the Spiral Head Nebula on old, recommissioned ships. Following the death of most of the crew of one such ship during the testing of a Kirlian Field Harness, Captain Kelly was returned to Earth by the Tenth Doctor in order to get Earth Corp to pay for what they had done. Following the outbreak of this scandal, Earth Corp "pledged to reform".(COMIC: The Ghost Ship)

Behind the scenes
According to Lance Parkin's Whoniverse: An Unofficial Planet-By-Planet Guide to the Universe of the Doctor, from Gallifrey to Skaro, the script for Into the Dalek specifies that the story takes place in the 31st century.