Thanks for your replies.
Thinking about this, maybe it's hasty to blame the poor ICC, when this could have been an issue somewhere else in the system. But I think it is clearly BMI's mistake. TG gave me two print-outs, one showing my itinerary according to the PNR, and one showing the itinerary according to the ticket number. The first had the domestic flight included; the second did not.
So this does look like a very odd situation where one sector of several just wasn't ticketed. And, it wasn't last leg as the thread title now states, it was the third leg of five.
I contacted BMI through the "Complaints" form on the website: how long do they usually take? The automated reply said they aim to reply within 2 working days and it's been way longer than that.
Oh, and the £300 figure is the walk-up J-fare for 2 passengers travelling CNX-HKT.