What is the typical structure and location of a check valve in a floor pump?
I managed to fix it! The only valve like thing I could find in the pump was a small bit of brass tubing, but it was hollow all the way through so figured there must a small ball that is displaced when air goes in to the tyre but falls back preventing air going the other way. My partner miraculously found it in the sink. It looks like this:



It goes in the base here:



On top of that goes the metal tube that runs up the side of the piston tube:



Thanks for the replies. I love it when I manage to fix the consequences of my own idiocy.