The most important thing whether UK or abroad is to supply the manufacturer with all the data they require in the right format with some explanitary notes, and if possible a fabrication drawing.
You only end up talking to manufacturers if there is a problem with the data, get that right and the rest is easy.
China, prices are currently lower than UK, again correct data no problem.
Basic Data:
Fab drawing with instructions such as solder resist, solder resist colour, copper weight, track and gap, silk screen, number of layers.
Gerber artwork data for each layer in same format and alligned.
Excellon drill info, same format as gerber data.
IPC-D-356 netlist if system allows.