Out of curiosity, I recently watched this BBC documentary, which stated rather outright that there was a genuine concern amongst certain members of the military and secret service that Wilson's Labour government would turn communist, or else otherwise prove ineffective in preventing rising social unrest in the country. The documentary linked the coup's planners to a smear campaign against Wilson and his cabinet in the press, as well as the army's deployment at Heathrow in 1974 as a form of 'dress rehearsal' for the planned occupation of London.
I'm a tad skeptical; it all sounded a bit Seven Days in May to me, and as yet, I've not found a source, beyond wikipedia, backing up the claims made in the documentary. Any historian of modern British politics willing to shed some light on the matter?
This is a bit difficult to source for me, the only brief write-up I have on this is from a Do Or Die anthology, from 2003, however it does mention other sources.
I'll just reproduce what it says, verbatim: "The 1970s crisis and the secret state destabilisation of a succession of Labour governments is a rarely mentioned but extremely important part of recent British history: "A substantial section of the British Secret state and its allies in the Conservative party, business and the media believed, or found it useful to pretend to believe- the distinction is difficult to make- that British democracy, the state, and even the capitalist system itself was under threat from a resurgent left, spearheaded by the trade unions and manipulated by the British Communist Party under instruction from Moscow..."- from Lobster Magazine No.34, p.32.
Radical right militias led by intelligence and military men were formed. Newspapers openly discussed the right circumstances for Army intervention in Britain while MI5 orchestrated black propaganda against the Labour Cabinet and trade union leaders. Joint military and police operations were carried out at Heathrow Airport without government sanction. Plans were advanced to install an unelected government of "National Unity" lead by Lord Mountbatten. No unsubstantiated conspiracy theory, this was first exposed in an autobiography by an ex-Daily Mirror executive who was actually at a meeting with some of the conspirators and a long time MI5 agent. Similar manoeuvres within the military continued through to the mid 70's.
The parapolitical background to the '70s crisis is essential to any understanding of the death of the post-war consensus and the triumph of the Thatcherite radical right. It's amazing to realise how near to the brink Britain really was. See Who Framed Colin Wallace? by Paul Foot, (Macmillan, 1988) and, Smear: Wilson and the Secret State by Stephen Dorill and Robin Ramsay, (Fourth Estate). These are still the best and most fully documented accounts of the Wilson plot".
You can judge of these source's credibility for yourself, but in my opinion Robin Ramsay, who started Lobster magazine (https://en.wikipedia.org/wiki/Lobster_(magazine)) is a pretty credible writer. The contents page for the issue of the Lobster mentioned is here: http://www.lobster-magazine.co.uk/issue34.php
I haven't read his book about Colin Wallace, but Paul Foot was also a reputable and award-winning journalist who I don't think would get involved in paranoid conspiracy stuff.
So in conclusion, the answer to your question is, I don't know, but it seems plausible based on these sources, which are admittedly sparse, but one would expect that given the secretive nature of the events.
On a personal note, (and this will probably be dismissed as anecdotal evidence), my father was a miner and local secretary of a left party in the 70's, and has told me about how extremely paranoid the security services were about the unions at the time. He claims, for instance, to have had his mail opened, presumably by MI5 or someone working for them by proxy. This isn't actually as far-fetched as it might sound.
Another source I should mention is Peter Wright's "Spycatcher", which also apparently mentions these events, and was initially banned in Britain. (Or, at least, the British government attempted to ban it).
This post is tagged as "British Army in the 19th century" yet refers to the 1960's and 1970's... a slip of the keyboard maybe?