Sandpaper to a flat surface is a pain, but also very simple. It’s worth to check the sole with a straightedge and mark any hollows or high spots. Then, if you do have a curve on the sole, you can buy sand paper in roll form (usually used for the large floor sanders) and use that on a non-textured piece of kitchen worktop to give a longer flatter area. You could also fix your wooden plane with this as well. You don’t need to glue the sandpaper to the worktop, just restrain it so that it does not move. This also means that you are left with a reasonably reliable flat plate that you can use for levelling chair legs etc. if your workbench is not perfectly flat (just remember to store it vertically).
My local Obi sells offcuts, but I am not sure what happens in other big box stores in other countries (take or buy a long ruler and check the worktop for flat before you buy).
I have had success with this in the past. (Also, I usually use fresh new pieces of MFC as mounting for sanding at 1500 and 2500 grit on some of my blades and chisels.)