airline recomondations for china to UK?

Can anyone advise me some airlines to fly from Chongqing (China) to Manchester (UK)?
"Cheep as chips" if possible

I seriously doubt you will find one airline connecting these cities. You need an airline search engine.

Only flights within China or to east and southeast asia from Chongqing International airport.
You might fly from Chengdu to Amsterdam with KLM and get a cheap onward flight from there.
Otherwise, fly to another city which connect to the UK directly, check the Manchester Airport for details about airlines flying long distance.

My favorite Airline, Asiana, flies to Chongqing via Seoul, and they also fly out of LHR