Just looked through Sturtivant's*
RAF Flying Training and Support Units Since 1915 and there isn't anything I can add to Annie's post. The British Overseas Airways looks to be an excellent match, especially for an ex-Lancaster pilot who would be able to fly the Lancastrian. I've read a number of memoirs of ex-RAF pilots who found themselves rejected by the civilian airlines after the war because the airlines were a lot more strict and hierarchical in their outlook and attitudes.
Well done Annie - good research (but then again I knew that from your posts on t'other forum

)
* I would just like to add that Ray passed away last weekend after an illness. RIP, Ray, and thank you for your fantastic contribution to the history of the RAF and FAA.