diff --git a/wagtail/core/blocks/field_block.py b/wagtail/core/blocks/field_block.py
index 294531b4da..661df83183 100644
--- a/wagtail/core/blocks/field_block.py
+++ b/wagtail/core/blocks/field_block.py
@@ -1,5 +1,4 @@
 import datetime
-from html import unescape
 
 from django import forms
 from django.db.models.fields import BLANK_CHOICE_DASH
@@ -8,10 +7,10 @@ from django.template.loader import render_to_string
 from django.utils.dateparse import parse_date, parse_datetime, parse_time
 from django.utils.encoding import force_str
 from django.utils.functional import cached_property
-from django.utils.html import format_html, strip_tags
+from django.utils.html import format_html
 from django.utils.safestring import mark_safe
 
-from wagtail.core.rich_text import RichText
+from wagtail.core.rich_text import RichText, get_text_for_indexing
 from wagtail.core.utils import resolve_model_string
 
 from .base import Block
@@ -573,9 +572,9 @@ class RichTextBlock(FieldBlock):
         return RichText(value)
 
     def get_searchable_content(self, value):
-        # Strip HTML tags to prevent search backend earch backend from indexing them
+        # Strip HTML tags to prevent search backend from indexing them
         source = force_str(value.source)
-        return [unescape(strip_tags(source))]
+        return [get_text_for_indexing(source)]
 
     class Meta:
         icon = "doc-full"
diff --git a/wagtail/core/fields.py b/wagtail/core/fields.py
index a8b4b7fc26..dfcc17e94e 100644
--- a/wagtail/core/fields.py
+++ b/wagtail/core/fields.py
@@ -1,12 +1,11 @@
 import json
-from html import unescape
 
 from django.core.serializers.json import DjangoJSONEncoder
 from django.db import models
 from django.utils.encoding import force_str
-from django.utils.html import strip_tags
 
 from wagtail.core.blocks import Block, BlockField, StreamBlock, StreamValue
+from wagtail.core.rich_text import get_text_for_indexing
 
 
 class RichTextField(models.TextField):
@@ -23,9 +22,9 @@ class RichTextField(models.TextField):
         return super().formfield(**defaults)
 
     def get_searchable_content(self, value):
-        # Strip HTML tags to prevent search backend earch backend from indexing them
+        # Strip HTML tags to prevent search backend from indexing them
         source = force_str(value)
-        return [unescape(strip_tags(source))]
+        return [get_text_for_indexing(source)]
 
 
 # https://github.com/django/django/blob/64200c14e0072ba0ffef86da46b2ea82fd1e019a/django/db/models/fields/subclassing.py#L31-L44
diff --git a/wagtail/core/rich_text/__init__.py b/wagtail/core/rich_text/__init__.py
index e90b37d333..63104f5778 100644
--- a/wagtail/core/rich_text/__init__.py
+++ b/wagtail/core/rich_text/__init__.py
@@ -1,5 +1,9 @@
+import re
+from html import unescape
+
 from django.db.models import Model
 from django.template.loader import render_to_string
+from django.utils.html import strip_tags
 from django.utils.safestring import mark_safe
 
 from wagtail.core.rich_text.feature_registry import FeatureRegistry
@@ -33,6 +37,17 @@ def expand_db_html(html):
     return FRONTEND_REWRITER(html)
 
 
+def get_text_for_indexing(richtext):
+    """
+    Return a plain text version of a rich text string, suitable for search indexing;
+    like Django's strip_tags, but ensures that whitespace is left between block elements
+    so that <p>hello</p><p>world</p> gives "hello world", not "helloworld".
+    """
+    # insert space after </p>, </h1> - </h6>, </li> and </blockquote> tags
+    richtext = re.sub(r'(</(p|h\d|li|blockquote)>)', r'\1 ', richtext, flags=re.IGNORECASE)
+    return unescape(strip_tags(richtext).strip())
+
+
 class RichText:
     """
     A custom object used to represent a renderable rich text value.
diff --git a/wagtail/core/tests/test_blocks.py b/wagtail/core/tests/test_blocks.py
index dba1062198..3d2cab35b0 100644
--- a/wagtail/core/tests/test_blocks.py
+++ b/wagtail/core/tests/test_blocks.py
@@ -558,11 +558,17 @@ class TestRichTextBlock(TestCase):
         result = block.get_searchable_content(value)
         self.assertEqual(
             result, [
-                'Merry Christmas! & a happy new year\n'
+                'Merry Christmas! & a happy new year \n'
                 'Our Santa pet Wagtail has some cool stuff in store for you all!'
             ]
         )
 
+    def test_get_searchable_content_whitespace(self):
+        block = blocks.RichTextBlock()
+        value = RichText('<p>mashed</p><p>po<i>ta</i>toes</p>')
+        result = block.get_searchable_content(value)
+        self.assertEqual(result, ['mashed potatoes'])
+
 
 class TestChoiceBlock(WagtailTestUtils, SimpleTestCase):
     def setUp(self):
diff --git a/wagtail/core/tests/test_rich_text.py b/wagtail/core/tests/test_rich_text.py
index ef0f1162e5..8376cafdf3 100644
--- a/wagtail/core/tests/test_rich_text.py
+++ b/wagtail/core/tests/test_rich_text.py
@@ -173,3 +173,13 @@ class TestRichTextField(TestCase):
         value = body_field.value_from_object(christmas_page)
         result = body_field.get_searchable_content(value)
         self.assertEqual(result, ['Merry Christmas from Wagtail! & co.'])
+
+    def test_get_searchable_content_whitespace(self):
+        christmas_page = EventPage.objects.get(url_path='/home/events/christmas/')
+        christmas_page.body = '<p>mashed</p><p>po<i>ta</i>toes</p>'
+        christmas_page.save_revision(submitted_for_moderation=False)
+
+        body_field = christmas_page._meta.get_field('body')
+        value = body_field.value_from_object(christmas_page)
+        result = body_field.get_searchable_content(value)
+        self.assertEqual(result, ['mashed potatoes'])