There are lots of low-cost direct flight options available: often you cannot find these on search engines, but you can by checking promotions on airlines’ own websites. To ascertain which airlines have direct flights from your preferred airport, you can check the airport on Wikipedia to see a list of all flights operating from there. Those coming to China from the UK should note that there are now direct flights to Beijing from Manchester with Hainan Airlines, very comfortable transfers from Birmingham with Etihad or Emirates and lots of options from London.
Please check out the following search engines to find the best rates. The top two are Chinese and so are usually the best for China flights:
- https://itunes.apple.com/cn/app/qunar-find-cheap-flights/id965784666?mt=8 (www.qunar.com is usually the cheapest site with the most route options—but it is only accessible in English as an App.)