For info BA still do codeshare with Aer Lingus on the LHR route, it's just EI won't put the bags through anymore in case they lose them and have to pay to return them to you!
I don't think it's a huge problem myself, pick them up on the walk to the heathrow express, 5 minutes later you're in T5. BA can be more expensive, the service is good and T5 is great though. Have a good hunt around, there are great bargains with lots of airlines at the moment. (would be a little nervous about China Airlines though!)
Enjoy China, it's a fab place..