In both cases the initial Cabinet reaction was hardline. When the pirate station challenged the Government's ability to control the airwaves, the Post Master General, Reginald Bevins, outlined two options: jamming the fledgling broadcaster (which ran therisk of interfering with legitimate broadcasts) and making it illegal for Britons to provide material support or advertising.
But two days later, Mr Bevins was backtracking. After a meeting of the backbench Broadcasting Committee a letter from Mr Bevins to the Prime Minister revealed that "backbenchers were in favour of the continuance of Radio Caroline" and were opposed "to any idea of legislation".
To his alarm some "even suggested that Radio Caroline should not only be tolerated but even encouraged".
The Caroline issue had been seized on by newspapers as an example of the need for local radio and many Tory MPs sided with a private, free market venture. Conservative disarray was reflected in a note of the Prime Minister's daily committee on 13 May: "It is vital that ministers should be clear as to our line about Radio Caroline. We run the risk of looking very foolish."
With the election looming the most practical solution was not to proceed with legislation against Caroline until the Council of Europe had examined the international aspects.
Meanwhile, with MPs calling for the return of birching, the Cabinet considered removing driving licences from Mods and Rockers who clashed in seaside towns at bank holiday weekends.
A letter from the Home Secretary, Henry Brooke, to the Prime Minister in June rejected the idea because, to be effective, magistrates would have had to have been given the power of disqualification for any offence. That, concluded Mr Brooke, would "provoke an unhelpful amount of controversy".
Instead, Mr Brooke proposed to amend the 1914 Criminal Justice (Administration) Act to increase from £20 to £100 the fines, and amounts payable in compensation, for those convicted of malicious damage. At the Foreign Office and the Ministry of Defence the best brains became embroiled in a thorny Cold War issue: should Chi-Chi, London's Chinese panda, be allowed a Russian mate?
On January 13 1964 London Zoo's Curator of Mammals first raised Chi-Chi's plight in a letter to Sir Solly Zuckerman, proposing to "negotiate with Moscow to arrange a meeting between our increasingly sex-starved female and their solitary male. (As you know, Chi-Chi's sexual cycles became abnormally prolonged and intense last year)."
At the Foreign Office Duncan Wilson, an official, agreed to arrange a formal submission adding that "it may have important results in exacerbating the Sino-Soviet dispute, and will of course be of interest to the Nato Council".
Rab Butler, the Foreign Secretary, noted the proposal could proceed, only for Nicholas Henderson, an official and future ambassador, to observe irreverently: "Unless you think Mr Robert Kennedy could interpose himself".
Moscow remained unimpressed. Its first reaction, according to the MoD on 26 February, was unfavourable, leaving Chi-Chi - for the time being at least - as sex-starved as ever.