I do not know how you managed to book this because
https://www.china-airlines.com/uk/en from LGW only allows Taiwan, Hong Kong, Oceania and Philippines to be selected as destinations no matter if you choose Round Trip / One Way or Multi-City / Stopover. That is why I tried calling the London sales office, I will try calling them again but I wonder if the phone robot puts me in a queue and then disconnects the call again.
Yes you need to choose Taiwan as the destination to/from London that's why I said you have to do multi-city.
First leg: LGW-TPE
Second leg: TPE-BKK
Third leg: SIN-TPE
Fourth leg: TPE-LGW
Do it as if you have a stopover in TPE, but just choose the very next flight/day and it should price accordingly.