diff --git a/Framework/PythonInterface/mantid/plots/utility.py b/Framework/PythonInterface/mantid/plots/utility.py
index 4e02c746b12961434f6a1d815bab46bf307c7321..2e69e98908026787bb9fc91965b4fe7410910aed 100644
--- a/Framework/PythonInterface/mantid/plots/utility.py
+++ b/Framework/PythonInterface/mantid/plots/utility.py
@@ -11,10 +11,17 @@ from contextlib import contextmanager
 
 from matplotlib import cm
 from matplotlib.container import ErrorbarContainer
+from matplotlib.legend import Legend
 
 from enum import Enum
 
 
+if hasattr(Legend, "set_draggable"):
+    SET_DRAGGABLE_METHOD = "set_draggable"
+else:
+    SET_DRAGGABLE_METHOD = "draggable"
+
+
 # Any changes here must be reflected in the definition in
 # the C++ MplCpp/Plot.h header. See the comment in that file
 # for the reason for duplication.
@@ -117,6 +124,14 @@ def get_autoscale_limits(ax, axis):
         return locator.view_limits(axis_min, axis_max)
 
 
+def legend_set_draggable(legend, state, use_blit=False, update='loc'):
+    """Utility function to support varying Legend api around draggable status across
+    the versions of matplotlib we support. Function arguments match those from matplotlib.
+    See matplotlib documentation for argument descriptions
+    """
+    getattr(legend, SET_DRAGGABLE_METHOD)(state, use_blit, update)
+
+
 def zoom_axis(ax, coord, x_or_y, factor):
     """
     Zoom in around the value 'coord' along the given axis.
diff --git a/Framework/PythonInterface/test/python/mantid/plots/CMakeLists.txt b/Framework/PythonInterface/test/python/mantid/plots/CMakeLists.txt
index dfc7e590e48fab793a5be6a9b9fd9423b9ebd128..e62034a5b8d1aa84d48c8f19bc094de220ebbef2 100644
--- a/Framework/PythonInterface/test/python/mantid/plots/CMakeLists.txt
+++ b/Framework/PythonInterface/test/python/mantid/plots/CMakeLists.txt
@@ -3,11 +3,9 @@ add_subdirectory(modest_image)
 # mantid.dataobjects tests
 
 set(TEST_PY_FILES
-  helperfunctionsTest.py
-  plotfunctionsTest.py
-  plotfunctions3DTest.py
-  plots__init__Test.py
-  ScalesTest.py)
+    helperfunctionsTest.py plotfunctionsTest.py plotfunctions3DTest.py
+    plots__init__Test.py ScalesTest.py UtilityTest.py
+)
 
 check_tests_valid(${CMAKE_CURRENT_SOURCE_DIR} ${TEST_PY_FILES})
 
diff --git a/Framework/PythonInterface/test/python/mantid/plots/UtilityTest.py b/Framework/PythonInterface/test/python/mantid/plots/UtilityTest.py
new file mode 100644
index 0000000000000000000000000000000000000000..94d4fd2a3550c3444f8c8e18712c67c786876f0a
--- /dev/null
+++ b/Framework/PythonInterface/test/python/mantid/plots/UtilityTest.py
@@ -0,0 +1,37 @@
+# Mantid Repository : https://github.com/mantidproject/mantid
+#
+# Copyright © 2019 ISIS Rutherford Appleton Laboratory UKRI,
+#     NScD Oak Ridge National Laboratory, European Spallation Source
+#     & Institut Laue - Langevin
+# SPDX - License - Identifier: GPL - 3.0 +
+#  This file is part of the mantid package
+# Mantid Repository : https://github.com/mantidproject/mantid
+#
+# Copyright © 2018 ISIS Rutherford Appleton Laboratory UKRI,
+#     NScD Oak Ridge National Laboratory, European Spallation Source
+#     & Institut Laue - Langevin
+# SPDX - License - Identifier: GPL - 3.0 +
+from __future__ import absolute_import, division
+
+import unittest
+
+from mantid.plots.utility import legend_set_draggable
+from mantid.py3compat.mock import create_autospec
+from matplotlib.legend import Legend
+
+
+class UtilityTest(unittest.TestCase):
+
+    def test_legend_set_draggable(self):
+        legend = create_autospec(Legend)
+        args = (None, False, 'loc')
+        legend_set_draggable(legend, *args)
+
+        if hasattr(Legend, 'set_draggable'):
+            legend.set_draggable.assert_called_with(*args)
+        else:
+            legend.draggable.assert_called_with(*args)
+
+
+if __name__ == '__main__':
+    unittest.main()