I would think that the pass letter is for your information only. If you have put in a C.A.F, then I would expect the next step would be an offer letter from your LEA. With the offer letter should be an option to go on the waiting list/s or appeal.
go back to your LEA and request that they explain the procedure and the anticipated time frame, preferably by email so you have it in writing.
Your LEA should co-ordinate with Medway but it wouldn't hurt to email Medway LEA and ask them to explain the procedure, for your situation.
Don't give up until you are satisfied you are clear about the admission arrangements for your DC.
As a late applicant you are already at a disadvantage, so depending on what school you get offered, it may be necessary for you to go on waiting lists and appeal.