Many of the Conservatives who voted for David Cameron last year would like the UK to leave the EU but they voted for him because he was the only Conservative candidate in the single-member constituency. Similarly, many of those who voted for Boris Johnson would like the UK to remain in the EU but they voted for him because he was the only Conservative candidate in the single-member constituency.
With STV in multi-member constituencies, Conservative (and, indeed, Labour and other) voters would have had a choice of candidates within their own party and they could have chosen between pro- and anti- EU candidates. They could also have chosen genuine “Don’t knows” who could have listened to the parliamentary debate before deciding.
The result would have been proportionate, not only between political parties but also between Remain, Out and Undecided. Then Parliament would have been representative of these views. It could have taken a considered decision on this complex question without resorting to a referendum, in which campaigners rely more on emotion than facts and exaggerate their claims (some would say, “lie”) and in which John and Jane Public are asked to make a very important decision without the time and resources to research the facts.