I'm very sorry this is so long, and also for namechanging, but everyone knows primary school catchments are such a sensitive area, so I really don't want to risk being outed...
We moved out of London last year, to get better quality of life (air, space, etc.) and schools, and also because we wanted to finally buy: the places we were renting kept being sold (all of them in a row, right back to when DD was a year), and we just couldn't face paying so much to buy so little in that London area.
In the new town, not a lot was moving, property-wise, so we eventually decided to rent again when we moved, so that we wouldn't risk a chain collapsing right before the school aplication deadline, and we got a long lease, so we couldn't be kicked out before school started, either!
Well, DD got into a school nearby, and we are happy with it, and just want her to settle there, as she is a very anxious and awkward child (keeping being moved on hasnt been good for her) and finds it hard to make new friends.
For months we looked for a house to buy and it seems DH's reseacrh about the area (a work colleague lives here) was totally inadequate, because not only was very little coming on the market, it was all crazy asking prices (don't want to say how much, for fear of outing where we are). DH has also found the commute a struggle due to the extra ?leg? from this part of town to the train. So we started looking closer to the centre, where the trains run from.
We've now found a house which is close to commuting links and a real fixer-upper, so much more reasonably priced and better value for money than anything else we have seen. However, it is further from school, and I'm not sure it would make it into the catchment for this school. Yet the owner is pushing to exchange this month/early Aug (long before school starts ? aaagh)! It also needs a lot of work before we can live there (electrics, plumbing, walls, floors ? all very old and possibly dodgy ? we don't have the survey yet), so we do have to buy well before our rental lease runs out (again, probably meaning at the latest, the week before September begins).
Our new borough wants you to be properly resident in the in-catchment place with all the supporting documentation in January before school starts (we were) and when school starts (we will still be living there, but our lease ends three and a half weeks after DD's Reception class starts ? maybe a month after the actual school start of term). Not sure extending the lease would help, either, as we are being pushed to complete/exchange, and there is the period of works to factor in, so the two ? ownership and lease ? would have to run along side one another for a couple of months anyway.
But when we notify the school of our change of address, they'll be able to look back at the Land Registry as early as October (three-month delay in reporting of transactions), and see that the purchase went through (in my worst imaginings) in July. Is that early enough in the school term to withdraw DD's place? It's an academy, so I understand that means it's its own admissions authority.
It doesn't help that I haven't taken to life here, being a SAHM in a place where you need to get in the car to get to most of the parks, which is a pain with a 4yo DD and new baby (who was born here); I haven't made many friends, and nor has my DD (whereas we had a great support network in London). It's hard not to feel carpet-bagger guilt given that I sometimes actually hate this place and wish we'd never moved! DD's not happy, either, but she's been uprooted now, and I can't bear to do that again to her (except to the new house, where she can have a mural on the wall of her bedroom and a wigwam if she wants
).
Sorry for that essay. Is anyone able to give advice on how the school/LA might view the date of our house purchase (especially given that it won't be inhabitable until after school starts, and given that our rental lease doesn't expire till October)? It's one of those hardline boroughs which will withdraw a place not just through fraud (which is right) but also even if it was offered through the LA's error. 
We did act in good faith with cutting our ties with London (much as I regret it), but the timing for this house is unexpectedly tight, and a nightmare!
Thanks for getting to the end of this!