diff --git a/lib/iris/cube.py b/lib/iris/cube.py
index f58a2ce607..140e4f7113 100644
--- a/lib/iris/cube.py
+++ b/lib/iris/cube.py
@@ -2561,7 +2561,14 @@ def _repr_html_(self):
         from iris.experimental.representation import CubeRepresentation
 
         representer = CubeRepresentation(self)
-        return representer.repr_html()
+        # Catch exceptions in the html repr rather than passing them,
+        # and so fall back to the default cube repr.
+        try:
+            result = representer.repr_html()
+        except (IndexError, ValueError):
+            result = None
+        finally:
+            return result
 
     def __iter__(self):
         raise TypeError("Cube is not iterable")
diff --git a/lib/iris/tests/unit/cube/test_Cube.py b/lib/iris/tests/unit/cube/test_Cube.py
index 11860cb278..a5a379ecba 100644
--- a/lib/iris/tests/unit/cube/test_Cube.py
+++ b/lib/iris/tests/unit/cube/test_Cube.py
@@ -2411,5 +2411,19 @@ def test_cell_method_correct_order(self):
         self.assertTrue(cube1 == cube2)
 
 
+@tests.skip_data
+class Test__repr_html(tests.IrisTest):
+    def test_bad_repr(self):
+        # If an html repr fails we don't want it to pass the error.
+        cube = stock.simple_3d()
+        with mock.patch(
+            "iris.experimental.representation.CubeRepresentation.repr_html",
+            side_effect=ValueError("Bad substring"),
+        ):
+            # Confirm the exception when we make the html repr is not returned
+            # by the cube method.
+            self.assertIsNone(cube._repr_html_())
+
+
 if __name__ == "__main__":
     tests.main()