In this story, the Brigadier has been retired from UNIT and teaching at a school since 1977. But the UNIT stories from the Third Doctor's time on Earth were set in the 1980s so the Brigadier should be much younger and still be working at UNIT from 1977 to 1983.
In the info-text on the DVD it states that the Brendon school is not named onscreen until a much later episode. This is incorrect. When Turlough swerves the Humber to avoid hitting the other car, he passes a pole with a white directional sign that clearly says, " Brendon School."