Most airlines make no claims to provide a quiet environment, so you get what you get.

BA specifically advertises First as 'A haven of calm'. As such I strongly believe that BA has a duty to at least try to deliver this. A 'no babies in F' rule and a code of conduct for everyone else in F would be a good start.

Yes, I am aware of how unpopular this position is, and before anyone asks, I do have children. However, it's not me advertising the feature and doing nothing to try to deliver it.