As a regular traveller to China I would answer as follows:
If BA launched new routes to China and Taiwan from LHR, would any of these destinations be viable?
Chengdu Shuangliu International Airport - Already discussed seems it is possible
Guangzhou Baiyun International Airport - Even though it is only a couple of hours from Hong Kong it is the heart of an economically strong province so would make sense yes.
Hangzhou Xiaoshan International Airport - No cant imagine a major demand
Nanjing Lukou International Airport - No less than an hours flying from Shanghai not a big airport would I imagine dilute Shanghai
Taiwan Taoyuan International Airport - Used to have Taipei, however would imagine the significant political problems it creates means no for now.
Wuhan Tianhe International Airport - Maybe some way off in the future not now.
Xiamen Gaoqi International Airport - As with Hangzhou doubt there is the demand
Xi'an Xianyang International Airport - As above.