How far out are you looking? CX blocks reward availability within ~1-2 weeks or so of departure, so in that situation you might need to call. CX is normally generous with award availability, although I assume they do release more to their asia miles members than other Oneworld carriers....
I still collect avios and use BAEC as my main program. I looked into CX Marco Polo club / Asia miles (they offered to status match me to their Gold, equivalent of BA silver/OWS) but it is a lot harder to earn/maintain status with them. As an example my current (leisure only) flight bookings for next TP year will earn me 920 TPs, which is a fair way towards BAEC Gold renewal - the same flights on CX will not even get me the 600 I need to requalify as CX Gold).
If you want to keep with Avios, then sign up for a
Dah Sing BA Visa - earning rate is 1 avios / 6 HKD, which at current exchange rate is getting close to 2 avios/£ (so better than the BA Amex), plus 10% off base fares for direct BA flight bookings.