Third country is part of a transit flight

hello, please can you advise if the following itinerary would be eligible for visa free. The third country (Korea) forms part of a transit flight back to the UK:
Depart London 24 June, Arrive Seoul 25 June at 15:50
Depart Seoul 25 June at 17:30, Arrive Tianjin 25 June at 18:25
Depart Tianjin 29 June at 10:15am, arrive Seoul 29 June at 13:00
Depart Seoul 29 June at 14:30, Arrive London 29 June at 18:50