That might actually give PM Callaghan or Healey an excuse to implement an Indira Gandhi style 'national emergency'. (At least that scenario is less ASBish than a military coup.)
This is probably one of the few non-ASB possibilities for a coup-like situation within the UK in the 1970's. Perhaps Callaghan and Healey form a centrist National Government with moderate Tories.
To get this to occur you would need there perhaps to be much more support for both the hard-left, such as Tony Benn and the hard-right, such as Enoch Powell in the mid-1970's.
In this scenario, believing that 'The centre cannot hold' as the saying goes, moderate Labour and moderate Tory politicians decide to suspend Parliament and establish some kind of semi-authoritarian National Government in order to 'safeguard' democracy from the extremes.
Perhaps Callaghan in the Prime Minister of the National Government and Ted Heath is the Deputy Prime Minister (or vice-versa). I do know that Ted Heath harboured hopes (or delusions, depending on your point of view) of returning to the Prime Ministership under some form of centrist government of Nationa Unity, into the early 1980's.
I say this is the one of the most plausible coup-like scenarios as I personally believe that only a broadly centrist authoritarian goverment would be able to get public support or more correctly, public acquiescence to its policies.