Unfortunately, I think there are a few things that go against you here.
Looked After Child
The definition of Looked After Child in the Admissions Code is:
"A looked after child is a child who is (a) in the care of a local authority, or (b) being provided with accommodation by a local authority in the exercise of their social services functions (see the definition in Section 22(1) of the Children Act 1989)." (Page 31)
Your Great Grandchild was never 'Looked After'. She went from her Mum to you informally for 1 month, then stayed with you under a SGO. There was never a point when she was accomodated by social services or placed in foster care. She was not a Looked After Child. This is a major issue with SGOs and kinship care.
The error was yours
You applied for the place stating that she was a Looked After Child. The SW wrote an email 'fully supporting' the place. The LA used the combined information to decide on Category One.
However, you ticked the wrong box, because your GGD was not a LAC.
The error was corrected before allocations day
Although the error was made, giving you Category 1, it was corrected before offers day and you never had a place allocated.
It is possible, though, that you have a case for appeal based on:
Expectation of place
You were given the impression that your GDD would definitely get a place because you were informed that you were allocated Category 1 priority and you weren't informed that you'd been downrated to Category 5. If you had been informed, you could have challenged the LAC status earlier and possibly had it confirmed prior to the allocations.
I think it would be very unlikely that you will win, to be honest. LAC is a legal definition, not a common sense one, and in the legal sense your GDD has never been a LAC.