VJO - Yes they are, but there are some ifs and buts. Para 1.50 of the school admissions code says:
1.50 Once an offer of a school place has been made it is only reasonable for an admission authority to withdraw that offer in very limited circumstances. These may include when a parent has failed to respond to an offer within a reasonable time or the admission authority offered the place on the basis of a fraudulent or intentionally misleading application from a parent (for example, a false claim to residence in a catchment area) which effectively denied a place to another child; or where a place was offered under co-ordination by the local authority, not the admission authority, in error. If a parent has not responded to the offer of a place within a reasonable time, the admission authority must remind the parent of the need to respond within a further seven days and point out that the place may be withdrawn if they do not.
What sort of school was the offer for? Was it a foundation or VA school? If it is, and the LEA made the offer on their behalf in error, then that would seem to fall under the bit of para 1.50 that I have highlighted. If it isn't a foundation or VA school then none of the circumstances listed in that para seem to apply, although you need to bear in mind that these are examples and not an exhaustive list. Even so - even where the LEA is correct in withdrawing the offer - there is case law which suggests that they should do so quickly, because otherwise parents are entitled to rely on the offer that's been made. Quickly is taken to mean within about 3 days.
I suggest that you write/email to the LEA and say that you do not accept that, in all the circumstances, para 1.50 applies to you and that they therefore have no basis for withdrawing the offer. Reinforce that by saying that even if they did have the right to withdraw the offer (which anyway you don't accept) they lost that right because they took far too long to do it. Point out that the supposed withdrawal of the place only came to light because you chased up the missing acceptance letter and so (presumably) you could have gone on for days or weeks believing you had a place at the school.
Where LEAs make mistakes (and the mistake here is the withdrawal of the offer) they are supposed to rectify them without making you go to appeal. Many LEAs do, though, insist on such cases going before an independent panel. If you do have to appeal, the panel will take note of the LEA's apparently chaotic (lack of) systems. Make sure you have copies of all letters and emails - especially the email which shows that you did not receive the rejection letter until many days after it was dated.