How long would Cameron had stayed in office if voters chose to remain in EU

[Chickpeas]

Cameron said he would serve a full second term but realistically he would have had to step down at least 6 months before the 2020 General Election in order for the party to elect a successor. He couldn't serve right up until just before the election as there would need to be time for a party leadership battle to replace him.

I suspect he would have announced his intention to resign for the summer recess of 2019, with the Conservatives electing a leader over the summer and Cameron resigning once that person was in place.

It might well not have been May who won the leadership under such a scenario. Without the daunting prospect of Brexit many more candidates might have thrown their hat in the ring.  George Osborne was widely seen as a leading contender to succeed Cameron. His political fate was largely tied to Cameron as they were so close but if Cameron leaves office on a high it may well be Osborne who succeeds him. Boris Johnson probably would run too. There may also be a 'next generation' candidate especially if Cameron were to promote fresh faces to the cabinet in his last years as PM.