South Korea to UK

Yes, your itinerary if presented in its entirety is definitely and undeniably eligible for 144 hour visa free transit in wider Shanghai area and you do not need any kind of visa. It is advisable to have at least the first overnight in Shanghai booked in advance. When you land at Pudong airport the first thing you will do is to approach 24/144 hour visa free transit counter where you will apply for a temporary entry permit by presenting your flight tickets and accommodation booking confirmation. When your permit is granted, you will proceed to the immigration and then outside the airport to enjoy/spend your time in wider Shanghai area at your own. Have a nice journey.

If your entire transit time in Shanghai is shorter than 24 hours, you will be covered by 24 hour visa free transit, so no visa needed in this case as well. In any case, you are good to go.