The names of John Profumo and Christine Keeler refer to the 1963 Profumo Affair that rocked the British government. John Profumo, the Secretary of State for War in Harold Macmillan's government, and Christine Keeler, an aspiring 19-year model. The revelation forced his resignation and a widening scandal which resulted in the defeat of the Conservative Party in the 1964 elections.
Bacchus refers to "Hooray Henrys from the Bullingdon Club," which may be an oblique reference to the then (at the time of broadcast) prime minister David Cameron and colleagues George Osbourne, Boris Johnson.