When using the word consensus in a sentence, is it correct to say consensus on, over, or, of? For example if someone were to say,
In 1960s British politics, there was consensus [correct word] the National Health Service?
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You may be speaking of a consensus concerning or about or respecting or with regard to the NHS—that is, a general agreement about what that institution should do or what should be done with it, or something of that sort.
You may be speaking of a consensus in the NHS, some general agreement about something held by the officers staff of that institution. I daresay some might accept a consensus among the NHS in that sense; I wouldn't be very comfortable with that, but I'm not very knowledgeable about whether the NHS comprises in any sense a coherent body of people.
See the collocations of consensus with usage examples.
The example sentence is possibly not well-structured. Your only choice seems to be within for the given structure.
In 1960s British politics, there was consensus within the National Health Service.
It's "consensus on". I've just corrected it in an academic text for publication.
Other options are possible, for example a Google search for "consensus regarding" get half a million hits, whereas "consensus concerning"only gets 120,000 or so, perhaps because people don't like repeating "con-" twice in succession.
Trust me, I'm a translator :-)