Britain had some tremendous advantages as the leading warship exporter of the time, not the least of which is the industrial base is close to the yards.
I could see the US, France and Italy competing as well, and Japan is still a possibility at this point.
That said, the Chinese did do business with Austria-Hungary for the famous (and never completed) so-called '
China cruiser'
I would think Britain would win the contract;
Nelson and
Rodney are the newest, most powerful battleships in the world in 1928, and among the fastest battleships in the world at the time as well. Plus Britain has a modern 16in gun (experiencing teething problems at this point, but the Chinese don't know that). I doubt the Chinese would want the all-forward layout, but I'm sure British yards could design and 8 or 9 gun battleship with the 16in Mk I on 35,000 tons. If China wants a faster battleship or battlecruiser, the UK yards have experience there as well.
I could see the US offering a battleship using the 16in/50 Mk 2 and 3 guns for the never-completed
Lexington and
South Dakota (BB-49) classes at no cost, maybe even including extra guns as spares and for coast defense as an additional incentive. But a US-built ship would still be more expensive than one built in the UK. Japan might offer an updated
Nagato type on 35,000 tons. France and Italy would have to design a 16in to compete in caliber, though Italy did have the 15in/40 used in the
Francesco Caracciolo class.
My thoughts,