The nuclear power station is controlled by a LEO II.
Year of feature (shown above)
There are three LEO II consoles in this set. That's pretty amazing, given that the LEO Computers Society says there were only 11 LEO II installations!
Earlier Doctor Who episodes feature LEO II tape drives - the computer Zoe blows up in "The Invasion" (1968) is one, and there are several in "The Ambassadors of Death" (1970).
The consoles reappear in various modified forms right up until the Children in Need special "The Curse of Fatal Death" (1999), so in a sense the LEO II may be both the first and the last real computer to appear in the original series.