I'm puzzled about the start date too - DDs friend, with stronger appeal grounds than you mention, has lost an appeal for Vardean in August, & they are already over PAN so I can't understand how they miraculously found your DS a place at all 
I hate to worry you, but if you haven't Sussed it out already, our SA make mistakes - that's why we are in this mess too - though they lie & ass cover that though, so you won't know that if course.
I'm wondering if the reason that your DS didn't get a start at the beginning if term, is because there isn't actually a place for him at all & they are waiting for one to become available - I'm told there's usually some movement in the first 3/4 weeks of term with kids not taking up places offered as they've moved, gone to local private grammars etc - the SA forget to tell the schools that the place has been turned do?n too - this is not uncommon here apparently, hence why the school won't know yet - it would explain the late start, though I think it would also break rules as they are meant to allocate the places from the waiting list - but not sure our LA know what rules are - they make them up as they go along
Really sorry you are in this situation too, wish it could give you better news, but you really are lucky to have a Varndean start at al
try & relax, enjoy the extra holiday time - we've a heat wave coming, take your DS to Rottingdean beach, or Devils dyke & have some fun with him & try & calm him & tell him the benefits of a late school start - the other kids will have sussed out the personalities of his new classmates & teachers for him, they will soon fill him in with the gossip, so he gets to start school ahead if the game in that way
I'm afraid it's really all you can do is to keep him calm & look at the positives
Good luck