Although clearly intended to be set in the near future (Vaughn's collarless shirt and the video phone are nods in this direction), there is nothing else to suggest that The Invasion doesn't take place in the late 1960s. The Brigadier states the Yeti saga The Web of Fear took place 'nearly four years ago', but this is a subjective recollection rather than a precise statement of fact.
We suggest that this adventure took place in 1966 (shortly after the events of 'The War Machines') and that The Invasion takes place in the Spring of 1969, thus placing Spearhead from Space to Terror of the Zygons in the years 1969 to 1973. Mawdryn Undead states that the Brigadier retired in 1976 Therefore, Sarah Jane's claim to come from 1980 (Pyramids of Mars) cannot be accurate.
The fashions of the UNIT stories, The Invasion apart, are contemporary, although technological advances indicate humanity's [Cyber-aided] progress in this area has been greater than in the real world. Three things in particular date the UNIT stories: pre-decimal currency is in operation in Doctor Who and the Silurians, Mao-Tse Tung is still alive in The Mind of Evil, and there is a 1972 calendar in The Green Death. See also the individual stories for further dating.