What diameter pipe do I need to adjust this basin waste pipe?
Cut where marked, but adjust the location so you've got clearance to work later.

Seeing as you only need a couple of millimeters, you might be able to get away with buying only the coupling connector similar to this:



So a good straight cut where marked, insert the connect and solvent weld it back into place.  

Take the cut piece in with you, and just make sure you've got a snug dry fit in the store.
No need to actually figure out the exact diameter.  Just buy the piece that fits.