Transit from a country not of origin.

Yes, you can. Visa free transit has (almost) nothing with the visa policy of China and consequently the only detail that is really important is that the immediate points before and after your mainland Chinese stop are located in two different countries or eligible territories (eligible territories are Hong Kong, Taiwan and Macau) and that you hold a passport of the country that is eligible for 144 hour visa free transit. It is irrelevant where your immediate points will be in relation to your domicile (origin) country.

To conclude, your itinerary as you have presented it, is definitely eligible for 144 hour visa free transit in wider Beijing area and you are undoubtedly free to travel on UK passport. You should just take care that you do not have any additional landing within mainland China beside Beijing and you cannot return to Seoul immediately after Beijing. Have a nice journey.