If you do a dummy booking the taxes etc for an infant would amount to HK$1,420 (about £92). Heaven knows where the extra comes from. It would only be £37 more (i.e. £129 or so) for the infant in Y - but I can't see how the additional cost for J can be justified.

The whole 10% thing is a pet bug bear of mine as per this previous thread, but sadly it doesn't help the OP at all.

I hope you get a satisfactory resolution from another poster.

EDITED TO ADD: Playing around on ba.com further an infant in F prices out at HK$6,190+taxes, or £402 + the £92 in taxes + presumably the rest is for an off-line txn. So...they appear to be booking your infant into A in First Class.