diff --git a/docs/src/whatsnew/dev.rst b/docs/src/whatsnew/dev.rst
index 9ed3cb23c2..0ef6c7f65e 100644
--- a/docs/src/whatsnew/dev.rst
+++ b/docs/src/whatsnew/dev.rst
@@ -54,6 +54,10 @@ This document explains the changes made to Iris for this release
 #. `@rcomer`_ ensured that a :class:`matplotlib.axes.Axes`'s position is preserved
    when Iris replaces it with a :class:`cartopy.mpl.geoaxes.GeoAxes`, fixing
    :issue:`1157`.  (:pull:`4273`)
+   
+#. `@rcomer`_ fixed :meth:`~iris.coords.Coord.nearest_neighbour_index` for edge
+   cases where the requested point is float and the coordinate has integer
+   bounds, reported at :issue:`2969`. (:pull:`4245`)
 
 
 💣 Incompatible Changes
diff --git a/lib/iris/coords.py b/lib/iris/coords.py
index b236d407da..8bcba776fd 100644
--- a/lib/iris/coords.py
+++ b/lib/iris/coords.py
@@ -2440,7 +2440,9 @@ def nearest_neighbour_index(self, point):
         if self.has_bounds():
             # make bounds ranges complete+separate, so point is in at least one
             increasing = self.bounds[0, 1] > self.bounds[0, 0]
-            bounds = bounds.copy()
+            # identify data type that bounds and point can safely cast to
+            dtype = np.result_type(bounds, point)
+            bounds = bounds.astype(dtype)
             # sort the bounds cells by their centre values
             sort_inds = np.argsort(np.mean(bounds, axis=1))
             bounds = bounds[sort_inds]
diff --git a/lib/iris/tests/unit/coords/test_Coord.py b/lib/iris/tests/unit/coords/test_Coord.py
index 43170b6c4e..5f707f91db 100644
--- a/lib/iris/tests/unit/coords/test_Coord.py
+++ b/lib/iris/tests/unit/coords/test_Coord.py
@@ -74,6 +74,11 @@ def test_scalar(self):
         target = [0, 0, 0, 0, 0]
         self._test_nearest_neighbour_index(target)
 
+    def test_bounded_float_point(self):
+        coord = DimCoord(1, bounds=[0, 2])
+        result = coord.nearest_neighbour_index(2.5)
+        self.assertEqual(result, 0)
+
 
 class Test_nearest_neighbour_index__descending(tests.IrisTest):
     def setUp(self):