diff --git a/app/broadcast_areas/__init__.py b/app/broadcast_areas/__init__.py
index 5e2df3292..c9e40ec89 100644
--- a/app/broadcast_areas/__init__.py
+++ b/app/broadcast_areas/__init__.py
@@ -1,3 +1,5 @@
+import math
+
 from notifications_utils.formatters import formatted_list
 from notifications_utils.polygons import Polygons
 from notifications_utils.serialised_model import SerialisedModelCollection
@@ -49,6 +51,10 @@ class BroadcastArea(SortableMixin):
             BroadcastAreasRepository().get_simple_polygons_for_area(self.id)
         )
 
+    @cached_property
+    def simple_polygons_with_bleed(self):
+        return self.simple_polygons.bleed_by(self.estimated_bleed_in_degrees)
+
     @cached_property
     def sub_areas(self):
         return [
@@ -68,6 +74,20 @@ class BroadcastArea(SortableMixin):
         # https://www.pivotaltracker.com/story/show/174837293
         return self._count_of_phones or 0
 
+    @property
+    def phone_density(self):
+        return self.count_of_phones / self.polygons.estimated_area
+
+    @property
+    def estimated_bleed_in_m(self):
+        if self.id.endswith(CITY_OF_LONDON.WARDS):
+            return 500
+        return 5_900 - (math.log(self.phone_density, 10) * 1_250)
+
+    @property
+    def estimated_bleed_in_degrees(self):
+        return self.estimated_bleed_in_m / Polygons.approx_metres_to_degree
+
     @cached_property
     def parents(self):
         return list(filter(None, self._parents_iterator))
@@ -109,6 +129,13 @@ class CustomBroadcastArea:
 
     simple_polygons = polygons
 
+    @cached_property
+    def simple_polygons_with_bleed(self):
+        # We don’t yet have a way of working out the population  density
+        # of a custom area, so for now we have to use an average number
+        # to estimate the amount of bleed
+        return self.simple_polygons.bleed_by(Polygons.approx_bleed_in_degrees)
+
 
 class CustomBroadcastAreas(SerialisedModelCollection):
     model = CustomBroadcastArea
diff --git a/app/models/broadcast_message.py b/app/models/broadcast_message.py
index 763fc1e3c..e59e5f791 100644
--- a/app/models/broadcast_message.py
+++ b/app/models/broadcast_message.py
@@ -117,6 +117,17 @@ class BroadcastMessage(JSONModel):
     def simple_polygons(self):
         return self.get_simple_polygons(areas=self.areas)
 
+    @cached_property
+    def simple_polygons_with_bleed(self):
+        polygons = Polygons(
+            list(itertools.chain(*(
+                area.simple_polygons_with_bleed for area in self.areas
+            )))
+        )
+        # If we’ve added multiple areas then we need to re-simplify the
+        # combined shapes to keep the point count down
+        return polygons.smooth.simplify if len(self.areas) > 1 else polygons
+
     @property
     def reference(self):
         if self.template_id:
@@ -163,7 +174,7 @@ class BroadcastMessage(JSONModel):
     @property
     def count_of_phones_likely(self):
         area_estimate = self.simple_polygons.estimated_area
-        bleed_area_estimate = self.simple_polygons.bleed.estimated_area - area_estimate
+        bleed_area_estimate = self.simple_polygons_with_bleed.estimated_area - area_estimate
         return round_to_significant_figures(
             self.count_of_phones + (self.count_of_phones * bleed_area_estimate / area_estimate),
             1
diff --git a/app/templates/views/broadcast/macros/area-map.html b/app/templates/views/broadcast/macros/area-map.html
index 737cd24c0..04645eb2a 100644
--- a/app/templates/views/broadcast/macros/area-map.html
+++ b/app/templates/views/broadcast/macros/area-map.html
@@ -11,7 +11,7 @@
     </li>
     <li class="area-list-key area-list-key--likely">
       <span class="visually-hidden">
-        An extra area of {{ "{:,.1f}".format(broadcast_message.simple_polygons.bleed.estimated_area - broadcast_message.simple_polygons.estimated_area) }} square miles is
+        An extra area of {{ "{:,.1f}".format(broadcast_message.simple_polygons_with_bleed.estimated_area - broadcast_message.simple_polygons.estimated_area) }} square miles is
       </span>
       Likely to get
       <span class="visually-hidden">
diff --git a/app/templates/views/broadcast/partials/area-map-javascripts.html b/app/templates/views/broadcast/partials/area-map-javascripts.html
index 871145332..5a401b8fd 100644
--- a/app/templates/views/broadcast/partials/area-map-javascripts.html
+++ b/app/templates/views/broadcast/partials/area-map-javascripts.html
@@ -2,7 +2,7 @@
 <script>
   var polygons = []
 
-  {% for polygon in broadcast_message.simple_polygons.bleed.as_coordinate_pairs_lat_long %}
+  {% for polygon in broadcast_message.simple_polygons_with_bleed.as_coordinate_pairs_lat_long %}
     polygons.push(
       L.polygon({{polygon}}, {
         opacity: 1,
diff --git a/requirements.in b/requirements.in
index b92c25235..e2f3e95fa 100644
--- a/requirements.in
+++ b/requirements.in
@@ -24,7 +24,7 @@ Shapely==1.7.1
 awscli-cwlogs>=1.4,<1.5
 itsdangerous==1.1.0
 
-git+https://github.com/alphagov/notifications-utils.git@43.8.3#egg=notifications-utils==43.8.3
+git+https://github.com/alphagov/notifications-utils.git@44.0.0#egg=notifications-utils==44.0.0
 git+https://github.com/alphagov/govuk-frontend-jinja.git@v0.5.8-alpha#egg=govuk-frontend-jinja==0.5.8-alpha
 
 # gds-metrics requires prometheseus 0.2.0, override that requirement as later versions bring significant performance gains
diff --git a/requirements.txt b/requirements.txt
index 92fe0a526..351229bcc 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -110,7 +110,7 @@ mistune==0.8.4
     # via notifications-utils
 notifications-python-client==6.0.2
     # via -r requirements.in
-git+https://github.com/alphagov/notifications-utils.git@43.8.3#egg=notifications-utils==43.8.3
+git+https://github.com/alphagov/notifications-utils.git@44.0.0#egg=notifications-utils==44.0.0
     # via -r requirements.in
 openpyxl==3.0.6
     # via pyexcel-xlsx
diff --git a/tests/app/broadcast_areas/test_broadcast_area.py b/tests/app/broadcast_areas/test_broadcast_area.py
index 55955cbce..7c904ce55 100644
--- a/tests/app/broadcast_areas/test_broadcast_area.py
+++ b/tests/app/broadcast_areas/test_broadcast_area.py
@@ -1,3 +1,5 @@
+from math import isclose
+
 import pytest
 
 from app.broadcast_areas import (
@@ -10,6 +12,10 @@ from app.broadcast_areas.populations import (
 )
 
 
+def close_enough(a, b):
+    return isclose(a, b, rel_tol=0.001)  # Within 0.1% difference
+
+
 def test_loads_libraries():
     assert [
         (library.id, library.name, library.is_group) for library in sorted(broadcast_area_libraries)
@@ -272,3 +278,71 @@ def test_estimate_number_of_smartphones_for_population(
     assert estimate_number_of_smartphones_for_population(
         population
     ) == expected_estimate
+
+
+@pytest.mark.parametrize('area, expected_phones_per_square_mile', (
+    (
+        # Islington (most dense in UK)
+        'lad20-E09000019', 21_348
+    ),
+    (
+        # Cordwainer Ward (City of London)
+        # This is higher than Islington because we inflate the
+        # popualtion to account for daytime workers
+        'wd20-E05009300', 310_674
+    ),
+    (
+        # Crewe East
+        'wd20-E05008621', 2_078),
+    (
+        # Eden (Cumbria, least dense in England)
+        'lad20-E07000030', 25.57
+    ),
+    (
+        # Highland (least dense in UK)
+        'lad20-S12000017', 4.40
+    ),
+))
+def test_phone_density(
+    area, expected_phones_per_square_mile,
+):
+    assert close_enough(
+        broadcast_area_libraries.get_areas(area)[0].phone_density,
+        expected_phones_per_square_mile,
+    )
+
+
+@pytest.mark.parametrize('area, expected_bleed_in_m, expected_bleed_in_degrees', (
+    (
+        # Islington (most dense in UK)
+        'lad20-E09000019', 488, 0.00439
+    ),
+    (
+        # Cordwainer Ward (City of London)
+        # Special case because of inflated daytime population
+        'wd20-E05009300', 500, 0.00449
+    ),
+    (
+        # Crewe East
+        'wd20-E05008621', 1_752, 0.01574
+    ),
+    (
+        # Eden (Cumbria, least dense in England)
+        'lad20-E07000030', 4_140, 0.0372
+    ),
+    (
+        # Highland (least dense in UK)
+        'lad20-S12000017', 5_095, 0.0458
+    ),
+))
+def test_estimated_bleed(
+    area, expected_bleed_in_m, expected_bleed_in_degrees,
+):
+    assert close_enough(
+        broadcast_area_libraries.get_areas(area)[0].estimated_bleed_in_m,
+        expected_bleed_in_m,
+    )
+    assert close_enough(
+        broadcast_area_libraries.get_areas(area)[0].estimated_bleed_in_degrees,
+        expected_bleed_in_degrees,
+    )
diff --git a/tests/app/main/views/test_broadcast.py b/tests/app/main/views/test_broadcast.py
index 795d6e300..ba473e376 100644
--- a/tests/app/main/views/test_broadcast.py
+++ b/tests/app/main/views/test_broadcast.py
@@ -623,7 +623,7 @@ def test_broadcast_page(
         'Scotland remove',
     ], [
         'An area of 177,439.8 square miles Will get the alert',
-        'An extra area of 3,058.9 square miles is Likely to get the alert',
+        'An extra area of 6,392.3 square miles is Likely to get the alert',
         '40,000,000 phones estimated',
     ]),
     ([
@@ -640,8 +640,17 @@ def test_broadcast_page(
         'Penrith West remove',
     ], [
         'An area of 6.3 square miles Will get the alert',
-        'An extra area of 14.4 square miles is Likely to get the alert',
-        '9,000 to 30,000 phones',
+        'An extra area of 22.6 square miles is Likely to get the alert',
+        '9,000 to 40,000 phones',
+    ]),
+    ([
+        'lad20-E09000019',
+    ], [
+        'Islington remove',
+    ], [
+        'An area of 9.7 square miles Will get the alert',
+        'An extra area of 4.6 square miles is Likely to get the alert',
+        '200,000 to 300,000 phones',
     ]),
 ))
 def test_preview_broadcast_areas_page(
@@ -726,7 +735,7 @@ def test_preview_broadcast_areas_page_with_custom_polygons(
         for item in page.select('ul li.area-list-key')
     ] == [
         'An area of 722.3 square miles Will get the alert',
-        'An extra area of 1,402.5 square miles is Likely to get the alert',
+        'An extra area of 1,498.5 square miles is Likely to get the alert',
         'Unknown number of phones',
     ]