Not sure about every park, but I just double checked our PS at Crystal Palace (8:05 am) which happens to be on an EE day and the CM told me that the park would open at 8 for EE and that 8:05 was the earliest "available". Now whether that meant that everything earlier was booked or not, I don't know (we were having some communication problems...).
But he did mention I could get in before (I thinking of shooting for 7:30) the gates open.
So, I don't know if this helped or not, but this is what I found out.