Flying from HKG to ICN.

We are flying from Hong Kong to Seoul via Shanghai, please see flight details below.

All British passport holders, will we need a visa for our visits?

Do you think there is enough time for us to transit in Shanghai on our way from Hong Kong to Seoul? I was told that I'll need to re-check in in Shanghai to go from Cathay Pacific to China Southern.

CX 238S 05AUG FR LHRHKG HK4 1700 1155 #1
CX 368S 08AUG MO HKGPVG HK4 0840 1110
CZ 369L 08AUG MO PVGICN SS4 1500 1745
CZ 370L 11AUG TH ICNPVG SS4 1845 1945
KA 835S 13AUG SA PVGHKG HK4 1900 2135
CX 239S 27AUG SA HKGLHR HK4 1220 1810

Thank you and kind regards
Emma