Ask for a complete junk bike. You might get lucky. Just about anything will work for you that came out of Nottingham. It really doesn't matter how ugly it is either because it is amazing how they will clean up with a little bit of Oxalic Acid in weak solution.
Look for the brands on
this page here. Most of that stuff will work for you. If you can get it cheap/free and has a bunch of part you can at least get a Frankenbike running so you can ride it. Then you can replace stuff little by little with exactly correct parts later if you still want to make it perfect.