I don't know what's available in China, but in the US OSHPark has 4-layer boards with 5 mil trace/space and 18 mil vias (10 mil drill + 4 mil AR) for $10 per square inch for a set of 3. That should be fine for 0.8mm pitch BGAs, unless you need a bunch of impedance controlled traces, in which case the 4-layer and pre-preg thicknesses start to fight you. I can't imagine you are unable to beat those prices in China.