It seems impossible to find the exact date of the escape.  The Spanish raid certainly took place in June ("the dazzling June sunshine", Chapter VII) but we know little more.  All we can say is that it must have been quite late in June, because the Pride of Devon arrived "towards the end of May" (Chapter V), Blood was approached by Whacker at least several days later, it took "some three weeks" after that to find the wherry, and the escape was three days later still.