That is why BSA put the inspection cover on the back of the gearbox. You need to remove it and look inside while you put it in to 2nd gear. That will tell you what is not adjusted correctly. Could be shimming or the change mechanism is not adjusted correctly.
This M20 gearbox is not one of BSA's better designs. A bike like a Matchless or Triumph, has no shims and nothing to adjust. They just work!