Hey Bram.Vos, thanks for the bug report. I tried to verify what was going on, but I was able to cut down trees without the issue you described. When you press `u` to start woodcutting are you selecting a tile with glyph / tree on the map or an image of the tree in the "nearby items"? I think the message indicates you select the image, I don't recall there being an option to pick up an item by selecting the glyph. Could you confirm?
Edit: Was there a chance maybe that you pressed `p` for pickup instead of `u`?
You are right about the inability to move, after pressing `u` you enter a "woodcutting" state that allows you to select a tree. You can cancel it with esc or right mouse button if needed.