diff --git a/django/forms/boundfield.py b/django/forms/boundfield.py
index d0ddd9715b..7f40fbbbb4 100644
--- a/django/forms/boundfield.py
+++ b/django/forms/boundfield.py
@@ -248,7 +248,7 @@ class BoundWidget:
         return self.tag(wrap_label=True)
 
     def tag(self, wrap_label=False):
-        context = {'widget': self.data, 'wrap_label': wrap_label}
+        context = {'widget': {**self.data, 'wrap_label': wrap_label}}
         return self.parent_widget._render(self.template_name, context, self.renderer)
 
     @property
diff --git a/django/forms/jinja2/django/forms/widgets/input_option.html b/django/forms/jinja2/django/forms/widgets/input_option.html
index 3f7085a4f0..48cd65b93a 100644
--- a/django/forms/jinja2/django/forms/widgets/input_option.html
+++ b/django/forms/jinja2/django/forms/widgets/input_option.html
@@ -1 +1 @@
-{% if wrap_label %}<label{% if widget.attrs.id %} for="{{ widget.attrs.id }}"{% endif %}>{% endif %}{% include "django/forms/widgets/input.html" %}{% if wrap_label %} {{ widget.label }}</label>{% endif %}
+{% if widget.wrap_label %}<label{% if widget.attrs.id %} for="{{ widget.attrs.id }}"{% endif %}>{% endif %}{% include "django/forms/widgets/input.html" %}{% if widget.wrap_label %} {{ widget.label }}</label>{% endif %}
diff --git a/django/forms/templates/django/forms/widgets/input_option.html b/django/forms/templates/django/forms/widgets/input_option.html
index 3f7085a4f0..48cd65b93a 100644
--- a/django/forms/templates/django/forms/widgets/input_option.html
+++ b/django/forms/templates/django/forms/widgets/input_option.html
@@ -1 +1 @@
-{% if wrap_label %}<label{% if widget.attrs.id %} for="{{ widget.attrs.id }}"{% endif %}>{% endif %}{% include "django/forms/widgets/input.html" %}{% if wrap_label %} {{ widget.label }}</label>{% endif %}
+{% if widget.wrap_label %}<label{% if widget.attrs.id %} for="{{ widget.attrs.id }}"{% endif %}>{% endif %}{% include "django/forms/widgets/input.html" %}{% if widget.wrap_label %} {{ widget.label }}</label>{% endif %}
diff --git a/django/forms/widgets.py b/django/forms/widgets.py
index 50e41b59ec..566bdf25d6 100644
--- a/django/forms/widgets.py
+++ b/django/forms/widgets.py
@@ -621,12 +621,12 @@ class ChoiceWidget(Widget):
             'attrs': option_attrs,
             'type': self.input_type,
             'template_name': self.option_template_name,
+            'wrap_label': True,
         }
 
     def get_context(self, name, value, attrs):
         context = super().get_context(name, value, attrs)
         context['widget']['optgroups'] = self.optgroups(name, context['widget']['value'], attrs)
-        context['wrap_label'] = True
         return context
 
     def id_for_label(self, id_, index='0'):
diff --git a/docs/releases/2.1.txt b/docs/releases/2.1.txt
index b22f27dcd7..aa4c6b14a4 100644
--- a/docs/releases/2.1.txt
+++ b/docs/releases/2.1.txt
@@ -310,6 +310,15 @@ If you want to continue to allow those passwords to be used, you'll
 have to define the :setting:`PASSWORD_HASHERS` setting (if you don't already)
 and include ``'django.contrib.auth.hashers.BCryptPasswordHasher'``.
 
+Moved ``wrap_label`` widget template context variable
+-----------------------------------------------------
+
+To fix the lack of ``<label>`` when using ``RadioSelect`` and
+``CheckboxSelectMultiple`` with ``MultiWidget``, the ``wrap_label`` context
+variable now appears as an attribute of each option. For example, in a custom
+``input_option.html`` template, change ``{% if wrap_label %}`` to
+``{% if widget.wrap_label %}``.
+
 Miscellaneous
 -------------
 
diff --git a/tests/forms_tests/widget_tests/test_radioselect.py b/tests/forms_tests/widget_tests/test_radioselect.py
index d0a70c7953..0f85563a58 100644
--- a/tests/forms_tests/widget_tests/test_radioselect.py
+++ b/tests/forms_tests/widget_tests/test_radioselect.py
@@ -1,6 +1,6 @@
 import datetime
 
-from django.forms import RadioSelect
+from django.forms import MultiWidget, RadioSelect
 from django.test import override_settings
 
 from .base import WidgetTest
@@ -130,3 +130,16 @@ class RadioSelectTest(WidgetTest):
         </ul>
         """
         self.check_html(self.widget(choices=choices), 'time', None, html=html)
+
+    def test_render_as_subwidget(self):
+        """A RadioSelect as a subwidget of MultiWidget."""
+        choices = (('', '------'),) + self.beatles
+        self.check_html(MultiWidget([self.widget(choices=choices)]), 'beatle', ['J'], html=(
+            """<ul>
+            <li><label><input type="radio" name="beatle_0" value=""> ------</label></li>
+            <li><label><input checked type="radio" name="beatle_0" value="J"> John</label></li>
+            <li><label><input type="radio" name="beatle_0" value="P"> Paul</label></li>
+            <li><label><input type="radio" name="beatle_0" value="G"> George</label></li>
+            <li><label><input type="radio" name="beatle_0" value="R"> Ringo</label></li>
+            </ul>"""
+        ))
diff --git a/tests/forms_tests/widget_tests/test_select.py b/tests/forms_tests/widget_tests/test_select.py
index beba21fe2d..42de5b6e92 100644
--- a/tests/forms_tests/widget_tests/test_select.py
+++ b/tests/forms_tests/widget_tests/test_select.py
@@ -294,6 +294,7 @@ class SelectTest(WidgetTest):
                 'template_name': 'django/forms/widgets/select_option.html',
                 'name': 'name',
                 'selected': False,
+                'wrap_label': True,
             }, {
                 'value': 'cd',
                 'type': 'select',
@@ -303,6 +304,7 @@ class SelectTest(WidgetTest):
                 'template_name': 'django/forms/widgets/select_option.html',
                 'name': 'name',
                 'selected': False,
+                'wrap_label': True,
             }]
         )
         self.assertEqual(index, 0)
@@ -319,6 +321,7 @@ class SelectTest(WidgetTest):
                 'name': 'name',
                 'selected': True,
                 'type': 'select',
+                'wrap_label': True,
             }, {
                 'value': 'dvd',
                 'template_name': 'django/forms/widgets/select_option.html',
@@ -328,6 +331,7 @@ class SelectTest(WidgetTest):
                 'name': 'name',
                 'selected': False,
                 'type': 'select',
+                'wrap_label': True,
             }]
         )
         self.assertEqual(index, 1)
@@ -344,6 +348,7 @@ class SelectTest(WidgetTest):
                 'index': '2',
                 'name': 'name',
                 'type': 'select',
+                'wrap_label': True,
             }]
         )
         self.assertEqual(index, 2)