whether to accept or reject non ranked allocation

You have had some harsh but realistic responses OP. As others have said, accept the offer, it is an insurance that your child will have a school place in September, it is not mandatory that she takes the place in September if the waiting lists gain you another offer. And if all you know about the offered school is hearsay then do your own investigation, the school may have qualities you don’t know about.

In the meanwhile it is worth checking that the LA has all your address details recorded accurately, that you were considered under the correct criteria ( eg linked school,sibling link, LAC, baptism and attendance criteria if a faith school ) and that if you were refused on distance that the distance measured is accurate. None of the above are likely to have happened, but they could have so you might as well make sure.

As well as appealing, check that you are on the waiting list for all your original preferences AND investigate other schools that you might prefer to the allocated one that might have space / you might be high on the waiting list for.

Unfortunately you have been naive. The local authority are obliged to offer you a place, but it doesn't have to be at one of your listed preferences. If you reject their offered place then you will need to home educate or go private. If neither are an option, then your best bet is to accept the offered place but stay on the waiting list for other schools.

You are unlikely to win an appeal on the grounds you have stated. Imagine if everyone who was unhappy because they didn't get the place they wanted was able to do that?

You would need to have a very strong case for the curriculum at chosen school, and ideally only available at that school and with evidence that dc needs it, to make a case. Dismissing choices at the allocated school will not help.

If you reject it you risk having no place at all, if appeal and wl do not come through. It would not strengthen the appeal case to do so.

Do not reject the offer. I know 2 people that rejected a non ranked school offer (now year 8), 1 ended up with no school in September so had to be home schooled - still is a year later. 1 got a school but not until 1 week before School started and it was still not one of their preferences. Accept the place and stay on the wait lists but accept you might not get a different option.

Nothing you have so far mentioned sounds like a likely winning argument at appeal.

You need to find some strong arguments about why your preferred school would meet your child’s needs and why she would be disadvantaged if not given a place. Reading the very many appeal threads here may give you some ideas.

@sunnmoon if the LA demonstrates that the school is 'full', then the admissions appeal panel will need to decide if they can take any further pupils, and if they can, which pupils it can take. You could find yourself in a situation where your appeal case is being compared against 5 or 6 (or even more!) other cases, and only the strongest will win. So it isn't enough to say 'she'll be really sad' or 'the curriculum is better.' You need to be able to convince a panel that your DD needs that place so badly that it's more important that she goes to the school than any difficulty the school has with accommodating her, and that she is more important than any other child that has appealed.

Are any of the schools on your list your catchment school?

Yes as others say, you are best to accept the offered school. Doing so will not affect any appeal or WL offer. But if you reject it, your DC may be without a school place in Sept so you will need to either HE or go private.

The LA has offered you a place and it is not obliged to do anything else.

Re the appeal – the arguments that your DC is not happy and will be at a disadvantage (why?) will not carry weight. The argument about the curriculum is stronger but needs to be specific – for example, she is learning x language/has a grandparent that speaks it and it is only offered at the appealed-for school.

You say you were not allocated any of your preferences (note – not choices as there is no guarantee) – did you list your local or catchment school? Were all the schools you listed somewhat optimistic (as in, you wouldn't usually be offered) or were they more realistic – if the latter you may be high up on the WL and get a place that way.

Do not reject the offer. The Local Authority has fulfilled its legal duty by allocating a place and does not have to offer any other school.
There are two separate processes for getting a place in another school before September. The first is by appealing and the second is off the waiting list. The waiting list is held in oversubscription order and is a live one so late applicants will be slotted in the correct place and any changes eg a house move would change the place on the waiting list. No account is taken of the school you have been offered/if you have rejected it etc.

Appeal panels will take a view on whether you have had an offer (a legal requirement0 but generally would expect you to have an alternative (eg home educate) before rejecting the offer.

Do you mean that you were allocated a school that was not on the list you submitted? If so, accept the offer you were made and join the waiting lists for any of the schools you did list and would be happy with.

It’s a myth that rejecting the offer will somehow force the hand of the LA to offer a place elsewhere. It won’t. The LA has offered a place and therefore discharged its duty. That means that if you refuse it, they have no obligation to find you somewhere else and you’ll be on your own.

What are your grounds for appeal. You have to show that the detriment to your child not being offered a place, is greater than the detriment to the school of accepting a pupil over numbers.