>[The Conservatives promised a referendum] iff the renegotiations with Brussels failed, which they did.

No. The Conservative party promised an EU membership referendum by 2017 in its 2015 manifesto. That was not conditional on a failure of renegotiations. Nor, indeed, did David Cameron even concede that the renegotiations had failed, so that can’t possibly have been his stated reason for calling the referendum.

You can check the summary of the manifesto at https://www.bbc.co.uk/news/election-2015-32302062, or page 30 (printed page number) of the original document at https://www.barnetconservatives.co.uk/sites/www.barnetconser....

Another clear indicator can be found in this article: https://www.theguardian.com/politics/2016/jan/10/david-camer.... Here, Cameron is directly quoted as saying:

> My policy is to hold a renegotiation and then a referendum. That is what we promised in the manifesto and then to abide by what the British public say.

So you can see that there was never any suggestion that the referendum would be called or not called depending on the outcome of the renegotiations.