Originally Posted by NickB

I did not read it that way. What I read that as saying was that this was the best solution for everybody, not that the OP was demanding that. Doing this would result in nobody other than a parent sitting next to one of children. I would not particularly relish being sat next to a young child on a long-haul flight so I would also agree with the OP that this would be the best solution, not as something that BA should do for him but as the best solution all round for everybody.

In terms of what the OP expects, it seems to me that there is nothing in what the OP wrote that said that he expects that to happen, merely that he expects that every child in the party should be sat next to at least one adult in the party.