Best flight routes are via Seoul with Korean Air, via Moscow with Aeroflot, from Berlin with MIAT, or via Beijing with any number of carriers, with MIAT or Air China flying daily from Beijing. Turkish Air is another option which is cheap, at c.£800 from London, but the luggage allowance is rubbish, you touch down twice en route which allows them to fly you on short haul planes. In short you need a strong constitution to arrive in good shape.
From London you can expect to pay £1200-£1500 for Korean Air, or £900-£1200 for Aeroflot.
MIAT is around the EUR 1000 mark from Berlin.
Some 2015ers reported a good service with Turkish Air after all. the good thing about going all on a single carrier is that your luggage is marginally less likely to get lost. Or, to be more specific, it's as likely to get lost but it will get retrieved and sent on much faster.
A smart option is Round The World Experts, who do a lot of our flights wrangling for us here at Adventurists Towers. They have pretty competitive prices and they have a free ‘Travel Butler Service’ which enables you to change departure flights without being charged hefty penalties, they call the airline and investigate alternative flights and you just pay the alteration fee. If you purchase fully flexible tickets you can even change to a completely new airport.
To get a callback with some price info you can reach them on:
firstname.lastname@example.org or call 0844 560 9852.