http://www.dailymail.co.uk/tvshowbiz...r-500-000.html
15th of August for CBB according to The Daily Mail
So if true either Sunday the 3rd of June (if it's 10.5 weeks like The Guardian say) or Sunday the 10th of June / Monday the 11th of June (if it's 9.5 weeks like Marcus Bentley says) for BB13 if it finishes the night before.
EDIT - The Apprentice ends on the 3rd, so it won't be then, might be the 4th but that's a bank holiday.