School have revoked offer - not sure what to do next.

Renovation is a red herring. That wasn't the question.

The question was where is the child living and it was somewhere else.

This is really odd. How do they know? Someone must have reported you. Or has the council alerted them as you are paying council tax at two addresses?

Anyway, you'll need to ask the school what proof they will accept that you have moved in.

The school is legally required to follow its own admissions criteria. This means it has to go off where your child actually resides (assuming you were applying on distance and not on other criteria eg sibling/exceptional need etc). It is not allowed to be flexible on the application of the rules no matter how sympathetic it may feel.

Otherwise others who didn’t get in would quite rightly be aggrieved and could themselves appeal as the school would not have followed its own admissions criteria.

If you are registered with the council tax to be living there and are paying, then legally you do live there. Where you sleep won't impinge on that.

Not correct, the child needs to reside there, and OP may well need more than bills to prove that - especially in this situation ie where the OP said DC lived there when DC in fact didn’t.

I am not suggestting you did anything deliberately wrong but you applied from an address you were not living in and it seems that you were offered a place based on living there so now its been withdrawn.
There is nothing to lose by applying but I doubt you have grounds

Can you not inform council tax you've moved in and pay from that date at your new address. Put up beds in your new address. Meet the school to get that decision revoked, if they are at all reasonable, and have your place secured for September. If you are registered with the council tax to be living there and are paying, then legally you do live there. Where you sleep won't impinge on that.

I don’t see any grounds to win an appeal here tbh. You are not living at the address applied from and never were. There has been no admissions error.

As I said above I would move in asap. Water can be turned back on. Is there a toilet and somewhere to wash? Can you rig up cooking facilities?

Every day that goes past there is potential for more places to be given off the waiting list ahead of you and after a certain point there will be no more movement on the WL. So even if you get to the head of WL in July after works finish, there may be no spaces that come up by then.

It depends on what your alternatives are I suppose but if this is the school you want, I would not risk waiting.

Move in. Even if you have to put up a tent in the garden - move in. Get your DCs address changed at GP, dentist, bank etc. pay council tax as living there. Register to vote there. Move in this week.

Where are you living currently?

If you are still in your old house I can understand why it might look dodgy. If you are somewhere clearly temporary I’d think that should help your chances as it doesn’t suggest admissions fraud.

Have you claimed any sort of council tax reduction for a home undergoing renovation or something?

I'd just start taking over what I could, ASAP, even if it's just a couple of rooms. Spend whatever time you can in it and tell the school you're in now.

I wouldn't have thought they'd be going round everyone's house though, that's quite odd. Do you know anyone who didn't get a place while your DC did, and was aware of your house issues? I'd be getting a Ring doorbell and maybe a camera to see who's having a nosy!

This seems strange! How would they know?? What about children who are already at the school but then if you renovate and move out temporarily — it’s not really any different!!?
Id move in whatever that meant. You can always ‘move out’ again temporarily. Tell them - if they ask! - that there’s been an issue with the work and somethings being redone. I don’t think this is much of their business tbh; if you genuinely are going to live there and own the property I can’t see the problem.

bear in mind that any appeal lodged now will almost certainly be heard in September unless you're very very lucky. So you can appeal, but also make sure your address is updated the moment you move in, to adjust your place on the waiting list.

You have 20 school days to appeal - if the offer was revoked today and you will move in before 18th July, submit the appeal on the day you move on the basis you are now living there.

Move in. Sorted.

This. Why in earth wouldn't you, rather then mucking around with appeals and possibly losing a place. Very few houses are inhabitable, you don't tend to get mortgages on those.

just "move in" put a few things in - how are they going to prove it if you go off and sleep somewhere else every night! just pop by regularly and come out the door a few times

You should definately appeal - you have nothing to lose, and you didn't intend to mislead the school about your address. You may not win the appeal, but nothing lost by trying.

Sorry but how did you not know work needed to be done? Surely you got a survey?

I'm so sorry - what a nightmare situation! You've done everything right and been completely transparent. I came across this article that has some helpful information on appeals and what to do when you don't get your chosen school: https://www.twinkl.co.uk/news/when-do-parents-find-out-about-secondary-school-places-and-what-to-do-if-you-dont-get-the-school-you-want
I hope it helps and good luck! 💕