Since David Cameron has indicated he is going in October, and Article 50 will not be invoked until the new PM has been chosen, he has passed the buck to his successor, who may, or may not, invoke A50. Pressure will be on to do either.
Instead of calling another referendum, why don't they just dissolve parliament and hold a general election, with one party(ies) campaigning on Brexit, the other(s) on Bremain? I suppose they won't do that as they will then see themselves out of a job...