I would obviously would now have to pay to ensure my 7 & 5 year daughters sit next to a parent. I would rather fly with somebody else.
Right Way Up, In BA (and in many others), children under 12 will ALWAYS be seated next to an accompanying adult. Even if the group or family is split, no children under 12 who are travelling with parents/guardians are to be seated on their own. Even gold card holders would be moved, and if they don't like it, they can fill in a complain form, but, as I said, your daughters HAVE to be seated next to, at least, one of the adults they are travelling with.
In the terms and conditions of travel of most airlines, you will find a clause that says that airlines can move passengers (even with pre allocated seats, or even with prepaid seats, obviously refunded) whenever they need it for operational reasons, like children under 12 separated from their families, or trim restrictions, for example.