Do I qualify for 72-hour Visa-free Transit, I hold a British Passport

Itinerary below:
JFK (US) - Singapore (with a layover in HK)
Singore(3 days) to Australia
Australia(4 days) to Seoul (Korea)
Seoul (Korea) (1 day) to Shanghai (PVG)
Shanghai (PVG)(less than 24hr, overnight stay in hotel) to Hong Kong
Hong Kong(3 days) to JFk (US)