You might have caught MK primary admissions team on a bad day...
ds2 is in Y2 in an infant school and we were expecting to hear which junior school he'd got a place at on 16th April - national offers day (or whatever it's proper name is). Except the letter came this morning, complete with instructions on how to accept the place by logging onto the website - which you do and it then says offers to be sent out on 16th April.
I rang them up as obvious I wanted to accept the place there and then (first choice but ds1 is already there) while I was thinking about it and the website wasn't letting me. Hassled lady on the end of the phone was very apologetic and explaining that we weren't supposed to know but that some of the letters had been sent out early by mistake so we couldn't actually accept the place until 16th April when the website would be ready.
I'm guessing that I was not the first to ring to find out what was happening!
I think there is a significant pressure on lots of primary school places in MK at the moment as there's been an explosion of primary age kids that wasn't particularly expected (or at least wasn't well planned for) which is causing lots of problems. That's like to be exacerbated if parents like you have got an eye on senior schools that are changing their entry criteria so that being in the right feeder primary school will make a difference so will be looking to change asap when they wouldn't do ordinarily.
Not ideal but are there any other 'partner' schools that you could look at moving to in year that would enable you to send your dc to the academy you want her to go to? And I guess just keep ringing the school you want her to go to every week (and go and talk to them at the school reception so they 'know' you and you have a face and are a real person to them, rather than being just another disembodied voice at the end of the line) in the hope that something does come up.
And when ds1 was transferring from infants to juniors, a friend of his didn't get in but was hopeful that they'd get in once everything settled down so the mum home ed-ed the dc thinking it was just going to be for a week or two as in previous years there was usually enough flexibility in the system for that to have worked. However - by Christmas they'd gone from being something like 3rd on the waiting list to 45th, at which point she gave up. So again -because there are so many kids for the places, there's much less flexibility in the system than there used to be. 
At least if it is your catchment school you have an advantage in that you should be higher up the criteria if they do operate a formal waiting list or if you apply through ordinary Y2 to Y3 transition of places next year.
I've also found that in MK the local councillors and the parish councillors can be quite helpful. In my parish (and I assume that it's the same for others) there's a parish clerk that you can contact for advice about all sorts of things and he has contacts in the council to push for help when needed. And maybe one of those things could be to get a proper, fair, waiting list set up at the school if they don't have one. (And although they're called parish councillors which makes it sound like they're related to the local churches, they're not; it's just the smallest most local unit of local government and seem to cover a grid square or two in size on average).
Sorry not able to be very helpful in your situation though - but good luck.