I read somewhere recently that HKG is by far and away the biggest unserved destination in the Far East from BHX as well. I also know as a cast iron fact that CX have had talks with BHX in the past but as Skipness points out I doubt they want to dilute demand from LHR and MAN and year round front end traffic is key. The West Midlands has very strong business links with China through the car industry but this hasn't led to any flights being launched to anywhere in China. At EDI I should imagine demand for HK can be satisfied by the many one stop offerings through Europe or the sand pit.
As for CX if they see that people are happy to fly to MAN and catch a train to BHX, EDI and sonon, surely they will add extra frequency at MAN and xapitalise on their very successful operation there rather than all the costs associated with flying into a new airport and building up a new route from scratch? This is why they won't be seen at BHX for the foreseeable, if ever, I could see them at EDI but not right now...I am in HK this week and flew Swiss from BHX, despite the transfer in ZRH it was still more time and much more cost competitive than driving to MAN, parking my car for 10 days and flying CX from there and I can catch the train to BHX it's only a 20 min journey, although I know a lot of Midlander's do use the CX MAN flight so as ever it's horses for courses.
Just for info there were 8 other pax on my BHX-ZRH flight going to HK plus a similar number for SIN and a couple for Sao Paulo