I just did a really quick search on ba.com. its possible to go from csx-ctu, but you would have to route through HKG (from the availability I saw. I checked only 1 date and then clicked through the calendar until I found a date with availability. I found a second day with availability as well and the routing was the same). Doesn't look like you can go from CTU-CAN on BA.

Did you do a search on ba.com?