diff --git a/tests/tests/test_api.py b/tests/tests/test_api.py
index 937fd31..84ebafc 100644
--- a/tests/tests/test_api.py
+++ b/tests/tests/test_api.py
@@ -21,6 +21,8 @@
     PageWithStreamField, PageWithParentalManyToMany
 )
 
+from .utils import has_new_listblock_format
+
 
 # We could use settings.MEDIA_ROOT here, but this way we avoid clobbering a real media folder if we
 # ever run these tests with non-test settings for any reason
@@ -302,6 +304,8 @@ def test_rich_text_with_image_embed(self):
         ))
 
     def test_streamfield_with_page_links_in_new_listblock_format(self):
+        if not has_new_listblock_format():
+            self.skipTest("This version of Wagtail does not use the UUID ListBlock format")
         page = PageWithStreamField(title="I have a streamfield",
                                    body=json.dumps([
                                          {'type': 'list_of_captioned_pages',
diff --git a/tests/tests/test_import.py b/tests/tests/test_import.py
index cef8cad..6ea31d4 100644
--- a/tests/tests/test_import.py
+++ b/tests/tests/test_import.py
@@ -1,3 +1,4 @@
+from ensurepip import version
 import importlib
 import os.path
 import shutil
@@ -18,6 +19,8 @@
     PageWithRichText, PageWithStreamField, RedirectPage, SectionedPage, SimplePage, SponsoredPage
 )
 
+from .utils import has_new_listblock_format
+
 # We could use settings.MEDIA_ROOT here, but this way we avoid clobbering a real media folder if we
 # ever run these tests with non-test settings for any reason
 TEST_MEDIA_DIR = os.path.join(os.path.join(settings.BASE_DIR, 'test-media'))
@@ -715,6 +718,8 @@ def test_import_page_with_streamfield_rich_text_block(self):
 
     def test_import_page_with_new_list_block_format(self):
         # Check that ids in a ListBlock with the uuid format within a StreamField are converted properly
+        if not has_new_listblock_format():
+            self.skipTest("This version of Wagtail does not use the UUID ListBlock format")
 
         data = """{"ids_for_import": [["wagtailcore.page", 6]], "mappings": [["wagtailcore.page", 6, "a231303a-1754-11ea-8000-0800278dc04d"], ["wagtailcore.page", 100, "11111111-1111-1111-1111-111111111111"]], "objects": [{"model": "tests.pagewithstreamfield", "pk": 6, "fields": {"title": "My streamfield list block has a link", "slug": "my-streamfield-block-has-a-link", "wagtail_admin_comments": [], "live": true, "seo_title": "", "show_in_menus": false, "search_description": "", "body": "[{\\"type\\": \\"list_of_captioned_pages\\", \\"value\\": [{\\"type\\": \\"item\\", \\"value\\": {\\"page\\": 100, \\"text\\": \\"a caption\\"}, \\"id\\": \\"8c0d7de7-4f77-4477-be67-7d990d0bfb82\\"}], \\"id\\": \\"21ffe52a-c0fc-4ecc-92f1-17b356c9cc94\\"}]"}, "parent_id": 100}]}"""
         importer = ImportPlanner(root_page_source_pk=1, destination_parent_id=None)
diff --git a/tests/tests/utils.py b/tests/tests/utils.py
new file mode 100644
index 0000000..9011366
--- /dev/null
+++ b/tests/tests/utils.py
@@ -0,0 +1,6 @@
+from wagtail import VERSION as WAGTAIL_VERSION
+
+
+def has_new_listblock_format():
+    major, minor, *_ = WAGTAIL_VERSION
+    return major > 2 or (major == 2 and minor > 15)
\ No newline at end of file