The plane is an ordinary everyday Jumbo, with a bit of fancy painting on the tail where the BA crest usually goes. It is disguised in order to maintain the fiction that the airline does not serve Taipei, capital of Taiwan. If an airline wishes to fly to the People's Republic of China, it cannot serve Taiwan, too. So a pretend airline has to be invented, together with a pretend code.
BR flight 25 starts life from Heathrow as BA 25, but once in Hong Kong it becomes BR 25 for the onward hop to Taipei. (Conveniently, this is an old code left in BA's possession after it took over British Caledonian.)
Other airlines are equally circumspect about their operations to Taiwan. Qantas, for example, becomes Australia Asia Airways. But BA's global network means it is often necessary to use a British Asia plane in odd corners of the world, for example the Lusaka to Lilongwe route. Politics and travel do mix, but sometimes the results are baffling.