I take it you are not going to make a long stopover anywhere.

BA is excellent and it will be the shortest trip by way of LHR, you might even have enough time to take a shower in the lounge at LHR.

As far as service and ambiante I'd take Singapore Airlines.

Cathay is exactly as good, the new airport in Hong Kong is great and the lounge is an experience worthwile.

As far as the seats are concerned, Singapore and Cathay have wider seats. The nicest are with Singapore.

Have a grand trip