Is my repair to this plug safe?
That plug needs redoing. Urgently. It is unsafe.


  Make sure the clamp is on the covering for the cable not the
  individual wires


This is a correctly wired UK plug... different live &amp; neutral colours and there's a fuse, but you get the idea that the cable grip goes over the outer covering of the cable and is properly tightened. The exposed power wires (red and black in your picture) should be only as long as they need to be to reach the plug pins, no longer. The earth/ground wire (green &amp; yellow) should be a little longer, so it gets pulled out last if the cable grip fails. The bared copper should also be the minimum length needed to get under the screws, which should be fully tightened.