You may have seen this claim from a report by right-wing think-tank Policy Exchange doing the rounds - it's total demonstrable bullshit. Here's why (THREAD)
It's very loosely based on YouGov polling of 820 current and former academics here. YouGov questioned academics about their political views, here are the results (these are % of the sample). These results are perfectly sound https://docs.cdn.yougov.com/4lwd0ybm5c/BBResults_200423_Academics.pdf
As you can see, very few academics consider themselves right-wing. The breakdown of the raw numbers polled is:

6% of 484 current are fairly right wing
1% of 484 current are very right wing

10% of 336 former are fairly right wing
1% of 336 former are very right wing
This is where it gets stupid. When we're talking about current academics who are fairly or very right wing, we're talking about 7% of 484 people... 38 people. So when Policy Exchange says 32% of those 38 people say they self-censor, it means 12 told pollsters that they did.
38 people is so far from being a representative sample size that it is actually a joke, but this is the kind of rigour we are apparently dealing with. The figure is virtually meaningless and may as well be made up.
You can work out the margin of error: there are ~207,000 academics working in the UK (HESA). ~7% are right-wing, so our population size is 14,490. That gives a margin of error of 16%! As good as guessing, and within the margin of error of academics of other political persuasions
Appendix with other stupid things about this report: 1) The authors refer to ‘fairly right wing’ and ‘right wing’ but this wasn’t even what was polled for, it’s actually ‘fairly right wing' and 'very right wing’. 2) They inexplicably decided to treat ‘don’t know’ as ‘centrist'
But anyway, none of this stopped the claim getting on the front page of a national newspaper - job done
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