It's impossible to truly know the counterfactual, or what would have been necessary to trigger one or the other of a revolution or a coup. However, this seems deeply implausible given what actually transpired, and what happened in other, similarly developed countries. Paul Mason is being, at best, hyperbolic here. (If one checks the archive of his writings, this is hardly the first time.)

In historical context, trade union action was far more intense during the interwar (1918-38) period than during the 1970s, including Britain's only general strike in 1926. Unemployment was worse, as was inequality, poverty, and so on. This much more intense period of unrest led neither to a revolution, nor to a coup. Why, then, should we believe that there could easily have been one during the much less intense crisis of the 1970s? No other country in the developed world had one, though admittedly they were extremely common outside of Europe and the English speaking former settler colonies. Democratic channels were more than enough to absorb the rising discontent. While individual party governments were very fragile during that period, the system itself does not seem to have been at much risk of outright collapse.

There is some suggestion that there was a plotted military coup against Harold Wilson as early as 1974 which Wilson believed himself. He thought the military establishment and Royal Family were out to get him. Whether there's any truth in it, I doubt we'll ever know.

But it is possible that what Wilson did that angered the establishment was making concessions with trade unions to effectively keep the country together. In the wake of the oil crisis in 1973, Heath's government had brought in the three day week where electricity was effectively rationed after brinksmanship between the Conservative government and the NUM; Wilson "filled the gap" caused by strikes by offering the NUM an immediate pay rise to return to work, and the electricity came back on.