There are one direct and indirect flights connecting Liverpool and Beijing every week, with the journey taking 22 hrs 5 mins on average.
Or, if you're fairly flexible on dates, try to get a last minute-deal by regularly checking the Netflights website.
Beijing actually has one airports to choose from – but Beijing Capital Int. Airport (PEK) is the usually the cheapest option. If you need to fly into a specific airport, adjust your search to focus on those flights. The most popular airlines include Air China.
But if you can't find one which is right for you, try looking at flights to other cities in China to check out some other options.