Originally Posted by
giblet
Perhaps. But I have noticed that ITA prices are often incorrect for international fares, even when it's only one airline.
Following on from what
nux says, is the original (separate) MI fare shown on ITA if you price that sector alone?
If it isn't, then
nux's explanation covers that. If the lower MI fare is not published, then you're unlikely easily to get either BA or a travel agent to combine that on one ticket.
And in a case such as this, you have to be careful about what is "one ticket". Some travel agents will happily put itineraries like this onto one booking and give you one (agency) booking reference, but actually write the tickets separately. If they're separate tickets, you have no protection even if the agency put them onto a single booking.