This is one of those areas that to some extent is what is the "unofficial rule".
As a previously looked after child ( providing it was local authority looked after) then they by law they have to be at the top of the admission criteria. This in effect guarantees admission at the normal point of entry to a school, that is reception or year 7. However all it guarantees for an in-year admission, if the school was deemed to be full in that year group, would be to be top of the waiting list.
Section 3.9 to 3.15 of the admission guidance talks about the requirement for every LA to have a fair access protocol, which is for pupils who are vulnerable, having been permanently twice from schools, to get them back into school even if schools are full. Section 3.11 says that there is no duty for LAs to comply with parental preference when allocating places through the Fair Access Protocol, only that a place must be allocated in an appropriate school. The interesting bit is in 3.12 where it says "This provision will not apply to a looked after child, a previously looked after child or a child with a statement of SEN needs or an EHC Plan naming the school in question, as these children must be admitted." However it does not say that anywhere in the guidance as far as I am aware.
The reality is that all Local Authorities that I know of, have always read in to the guidance that looked after children and previously looked after children should be offered a place at a school that is requested, no matter what the numbers in the school year. There is also no question in my mind that any school appeal panel which had an appeal for a looked after child would admit because they are deemed the most vulnerable of children.There is simply no way that the school could make a case, in my opinion, that would outweigh the need to admit such a child. I have been on one panel where an academy refused, as the admission authority, to admit but the appeal hearing did not take very long!
One issue that you need to be careful about is that the child needs to have been previously looked after with the LA, if it was a private arrangement that does not normal count. You also need to check the detail at the bottom of the admission guidance page 10, which indicates how the children have been adopted, because there is apparently (and I do not know the detail) a loophole in that the admission law does not exactly tally with the law over adoption, so some adopted children are not officially covered by the admission guidance.
Sorry that got complicated.