Although not strictly a flying wing, as it is better described as tailless, Armstrong Whitworth had an un-numbered project design for a civil airliner in 1946 (There is a 3-view in Air Enthusiast but I haven't scanned that)
Then in 1947 and 1948 AW advertising featured a couple of speculative flying wing airliners that are probably based on concept design work undertaken in parallel with the AW52 and AW56 bomber projects.