On one occasion, he had an adventure with the Third Doctor and decided that the Doctor's morality was dangerous. He recounted his experience into a tape recorder and ended the recording by saying that the Doctor must be stopped. (AUDIO: Damascus)
Thorpe's forename wasn't given in Interference, but the common-sense interpretation of the passage is that the author was referencing Jeremy Thorpe.
He was explicitly mentioned in the "Party Politics" section of the BBC's Doctor Who site: "In the aftermath of several invasions of London in the late 60s, the 1970 election produces a hung parliament (conflicting Tory and Socialist policies towards the alien menace drive many voters towards the Liberals and fringe parties). In this atmosphere, a coalition government, led by Jeremy Thorpe, governs Britain in the early 70s." The article posits that continued alien invasions and "the power crisis caused by the collapse of Global Chemicals, the Government's involvement in the Axonite scandal and the Operation Golden Age fiasco, which included high ranking figures in the conspiracy" cause the coalition to collapse in 1973, and was succeeded by the Labour government under Shirley Williams. 
The Prime Ministers are listed in rough chronological order by their first term in office. Please note that this template only uses information from fictional sources. Real world information should not enter into this.