OK, the good news, unless this has changed recently, is that Cathay and BA comes into the same E terminal and though a 45 minute connection isn't great, it is do-able, assuming you don't have checked luggage or CX agrees to through check anyway. If you can get a boarding pass for PEK-LHR then so long as everything goes to time you should be OK, and I would plan on that happening. The problem with Cathay in particular over China is the airspace is congested, China's ATC imposes tight restrictions, the Chinese airforce has priority, and CX have huge problems getting flights to / from the mainland to operate on time. It's been like this for about 10 years now, it's just got a bit worse month by month by month.

From that point on I think you just have to play it by ear, unfortunately. The only 3 other thing I can think of is (a) ring Amex insurance on their call line to see if they can make any suggestions and (b) ring BA and ask them to put a note on the PNR to say you have been delayed by a cancelled CX service and (c) beg / ask Cathay to re-route via LHR direct instead. While on the Gold or USA line to BA you could see if they will reroute the to HKG service instead but I think that is unlikely to work out.