Was your booking marked with the infant on it properly? Friends of mine flew to Italy on BA the other week and when the mother (+infant) was selected in the OLCI map, the entire right of the plane, the exit rows AND the rows directly in front of/behind the exits were immediately greyed out to her.

You shouldn't have been able to move there in the first place based on that experience, so I'm quite surprised.

Incidentally, I get the exits (obviously) and right side (the lack of extra oxygen masks I assume) being greyed out but not the rows immediately before and after the exits I think they said it was a 734.