Maybe ten years ago I read this but I don't think it was a new book. Can't recall the cover. UK.
There's a pilot from alternative Earth where WW2 continued for decades, he's somehow stranded on our world and living like an amnesiac tramp for a lot of years (I think also, due to some mix up, he has a criminal record as a paedophile so is very unpopular whenever he has to interact with authorities).
He speaks in like 1940's British movie accent. At one point he had (different medical path) a female co-pilot who was just a head, a common practice after severe injuries.
This head had its counterpart in our world but whole bodied - I think other travellers from alt universe recognised her as the first one to have the head operation done.
There were various shenanigans that I don't recall much about - I want to say the pilots aircraft appeared in our world at a different date and astonished rescue workers due to a voice coming from a very small space. This was the head and she also spoke in 1940's accent/slang.
I think she and some scientists from our universe then went exploring across various alt universes and interacting with different people's along the way. Maybe to solve a mystery?
Towards the end she is reunited with the much older version of her pilot and I think they can then return to their plane ('plane' - see what I did there?)