From what our social worker told us, different LAs have different ways of doing it, if they do it at all...
Our LA just paid us a lump sum per child and didn't ask for receipts (although we kept them anyway just in case).
Some require it like an expenses form and some don't require evidence at all. Some LAs don't pay a grant at all apparently.
I know that's not very helpful, but it really does depend on your LA! we also ended up getting ours a couple of months after placement. Do keep chasing, it's amazing what can be "forgotten" (jist as an fyi, life savings and any pocket money should also be transferred to you, and every child in care should have about £700 plus any other saved money given to them for their savings once the AO is granted, so do pop a date in your diary to chase that too! Your kid is entitled to it, it is theirs so don't let them miss out.)
I wouldn't count on getting a grant very quickly- it seems to be misnamed, because by the time you get it, the kids are already settled enough to have needed the bed and mattress! We figured there would be delays, so budgeted to not have it by getting as much stuff second hand where possible and then using the money when we got it to buy other stuff that we wanted or needed but were not strictly necessary- so we invested in some reusable bed pads, reusable nappies, a foldaway futon for the bedroom so we could settle them in the night and be near them, nightlights etc adoption specific books, grow clocks, baby cams etc so that if we were asked to justify it we could.