diff --git a/docs/src/whatsnew/latest.rst b/docs/src/whatsnew/latest.rst
index ea4b52ce2a..d0aefd02c1 100644
--- a/docs/src/whatsnew/latest.rst
+++ b/docs/src/whatsnew/latest.rst
@@ -47,6 +47,13 @@ This document explains the changes made to Iris for this release
    :class:`~iris.coords.AuxCoord`, which avoids some specific known usage problems.
    (:issue:`4860`, :pull:`5020`)
 
+#. `@Esadek-MO`_ and `@trexfeathers`_ added dim coord
+   prioritisation to ``_get_lon_lat_coords()`` in :mod:`iris.analysis.cartography`.
+   This allows :func:`iris.analysis.cartography.area_weights` and
+   :func:`~iris.analysis.cartography.project` to handle cubes which contain
+   both dim and aux coords of the same type e.g. ``longitude`` and ``grid_longitude``.
+   (:issue:`3916`, :pull:`5029`).
+
 
 🐛 Bugs Fixed
 =============
diff --git a/lib/iris/analysis/cartography.py b/lib/iris/analysis/cartography.py
index f38e48354d..8dbad9c4e9 100644
--- a/lib/iris/analysis/cartography.py
+++ b/lib/iris/analysis/cartography.py
@@ -169,20 +169,25 @@ def rotate_pole(lons, lats, pole_lon, pole_lat):
 
 
 def _get_lon_lat_coords(cube):
-    lat_coords = [
-        coord for coord in cube.coords() if "latitude" in coord.name()
-    ]
-    lon_coords = [
-        coord for coord in cube.coords() if "longitude" in coord.name()
-    ]
+    def search_for_coord(coord_iterable, coord_name):
+        return [
+            coord for coord in coord_iterable if coord_name in coord.name()
+        ]
+
+    lat_coords = search_for_coord(
+        cube.dim_coords, "latitude"
+    ) or search_for_coord(cube.coords(), "latitude")
+    lon_coords = search_for_coord(
+        cube.dim_coords, "longitude"
+    ) or search_for_coord(cube.coords(), "longitude")
     if len(lat_coords) > 1 or len(lon_coords) > 1:
         raise ValueError(
-            "Calling `_get_lon_lat_coords` with multiple lat or lon coords"
+            "Calling `_get_lon_lat_coords` with multiple same-type (i.e. dim/aux) lat or lon coords"
             " is currently disallowed"
         )
     lat_coord = lat_coords[0]
     lon_coord = lon_coords[0]
-    return (lon_coord, lat_coord)
+    return lon_coord, lat_coord
 
 
 def _xy_range(cube, mode=None):
@@ -578,6 +583,11 @@ def project(cube, target_proj, nx=None, ny=None):
         An instance of :class:`iris.cube.Cube` and a list describing the
         extent of the projection.
 
+    .. note::
+
+        If there are both dim and aux latitude-longitude coordinates, only
+        the dim coordinates will be used.
+
     .. note::
 
         This function assumes global data and will if necessary extrapolate
diff --git a/lib/iris/tests/unit/analysis/cartography/test__get_lon_lat_coords.py b/lib/iris/tests/unit/analysis/cartography/test__get_lon_lat_coords.py
new file mode 100644
index 0000000000..612e5d8ecf
--- /dev/null
+++ b/lib/iris/tests/unit/analysis/cartography/test__get_lon_lat_coords.py
@@ -0,0 +1,114 @@
+# Copyright Iris contributors
+#
+# This file is part of Iris and is released under the LGPL license.
+# See COPYING and COPYING.LESSER in the root of the repository for full
+# licensing details.
+"""Test function :func:`iris.analysis.cartography._get_lon_lat_coords"""
+
+import pytest
+
+from iris.analysis.cartography import _get_lon_lat_coords as g_lon_lat
+from iris.coords import AuxCoord
+from iris.tests.stock import lat_lon_cube
+
+
+@pytest.fixture
+def dim_only_cube():
+    return lat_lon_cube()
+
+
+def test_dim_only(dim_only_cube):
+    t_lat, t_lon = dim_only_cube.dim_coords
+
+    lon, lat = g_lon_lat(dim_only_cube)
+
+    assert lon == t_lon
+    assert lat == t_lat
+
+
+@pytest.fixture
+def dim_aux_cube(dim_only_cube):
+    lat_dim, lon_dim = dim_only_cube.dim_coords
+
+    lat_aux = AuxCoord.from_coord(lat_dim)
+    lat_aux.standard_name = "grid_latitude"
+    lon_aux = AuxCoord.from_coord(lon_dim)
+    lon_aux.standard_name = "grid_longitude"
+
+    dim_aux_cube = dim_only_cube
+    dim_aux_cube.add_aux_coord(lat_aux, 0)
+    dim_aux_cube.add_aux_coord(lon_aux, 1)
+
+    return dim_aux_cube
+
+
+def test_dim_aux(dim_aux_cube):
+    t_lat_dim, t_lon_dim = dim_aux_cube.dim_coords
+
+    lon, lat = g_lon_lat(dim_aux_cube)
+
+    assert lon == t_lon_dim
+    assert lat == t_lat_dim
+
+
+@pytest.fixture
+def aux_only_cube(dim_aux_cube):
+    lon_dim, lat_dim = dim_aux_cube.dim_coords
+
+    aux_only_cube = dim_aux_cube
+    aux_only_cube.remove_coord(lon_dim)
+    aux_only_cube.remove_coord(lat_dim)
+
+    return dim_aux_cube
+
+
+def test_aux_only(aux_only_cube):
+    aux_lat, aux_lon = aux_only_cube.aux_coords
+
+    lon, lat = g_lon_lat(aux_only_cube)
+
+    assert lon == aux_lon
+    assert lat == aux_lat
+
+
+@pytest.fixture
+def double_dim_cube(dim_only_cube):
+    double_dim_cube = dim_only_cube
+    double_dim_cube.coord("latitude").standard_name = "grid_longitude"
+
+    return double_dim_cube
+
+
+def test_double_dim(double_dim_cube):
+    t_error_message = "with multiple.*is currently disallowed"
+
+    with pytest.raises(ValueError, match=t_error_message):
+        g_lon_lat(double_dim_cube)
+
+
+@pytest.fixture
+def double_aux_cube(aux_only_cube):
+    double_aux_cube = aux_only_cube
+    double_aux_cube.coord("grid_latitude").standard_name = "longitude"
+
+    return double_aux_cube
+
+
+def test_double_aux(double_aux_cube):
+    t_error_message = "with multiple.*is currently disallowed"
+
+    with pytest.raises(ValueError, match=t_error_message):
+        g_lon_lat(double_aux_cube)
+
+
+@pytest.fixture
+def missing_lat_cube(dim_only_cube):
+    missing_lat_cube = dim_only_cube
+    missing_lat_cube.remove_coord("latitude")
+
+    return missing_lat_cube
+
+
+def test_missing_coord(missing_lat_cube):
+    with pytest.raises(IndexError):
+        g_lon_lat(missing_lat_cube)