For the employer, a delay of 2 weeks ought not to be a big deal, and most companies would wait longer than that to get the right person. If they don't ask, you could just raise it by saying "I've heard you wanted someone to start as soon as possible, but I'm only available on Aug 13, is this ok?" It does need to be discussed however, as the employer has established the expectation already that you could start earlier.
Raising this sort of thing by email ahead of an interview is awkward and risks cancelling or delaying the interview, and gives other candidates a look in. It makes sense to do a good job selling yourself in the interview to get them "hooked", and then give them a little bit of bad news.
So if you were applying direct I would bring it up at interview. However as you are going through a recruiter, you already have someone whose job is to grease the wheels, and I would suggest raising it with the recruiter now, and discussing whether your recruiter should bring it up before the interview, or whether you should raise it at interview.