From TARDIS Index File, the free Doctor Who reference.
The planet Earth, under a repressive government, has a population of 100 billion people, most of them living on floating islands. It is a highly polluted planet. (DW: Colony in Space)
The education system is highly accelerated at this point, students obtaining certificates in a vast range of disciplines by the age of ten. They are taught by machines for one hour a week. In comparison, a 20th century high school is like a nursery. (DW: The Web Planet)
Most Earth colonies during this time are "terrible places". (NA: Christmas on a Rational Planet)
By this time The Beatles are considered classical music, and a memorial theatre dedicated to them existed in Liverpool. (DW: The Chase)
Aspirin tablets are no longer in common use. (DW: The Web Planet)
Humanity has the ability to travel in hyperspace with such journeys being common and commercial. (NSA: Judgement of the Judoon)
Vicki Pallister, companion of the Second Doctor, is native to this era.