diff --git a/swh/loader/bzr/loader.py b/swh/loader/bzr/loader.py
--- a/swh/loader/bzr/loader.py
+++ b/swh/loader/bzr/loader.py
@@ -264,11 +264,16 @@
         if self.repo is not None:
             self.repo.unlock()
 
-    def get_repo(self):
-        _, _, repo, _ = bzrdir.BzrDir.open_containing_tree_branch_or_repository(
+    def get_repo_and_branch(self) -> Tuple[repository.Repository, BzrBranch]:
+        _, branch, repo, _ = bzrdir.BzrDir.open_containing_tree_branch_or_repository(
             self._repo_directory
         )
-        return repo
+        return repo, branch
+
+    def run_upgrade(self):
+        """Upgrade both repository and branch to the most recent supported version
+        to be compatible with the loader."""
+        cmd_upgrade().run(self._repo_directory, clean=True)
 
     def fetch_data(self) -> bool:
         """Fetch the data from the source the loader is currently loading
@@ -304,19 +309,31 @@
             self.log.debug("Using local directory '%s'", self.directory)
             self._repo_directory = self.directory
 
-        repo = self.get_repo()
+        repo, branch = self.get_repo_and_branch()
         repository_format = repo._format.as_string()  # lies about being a string
+
         if not repository_format == expected_repository_format:
             if repository_format in older_repository_formats:
                 self.log.debug(
                     "Upgrading repository from format '%s'",
                     repository_format.decode("ascii").strip("\n"),
                 )
-                cmd_upgrade().run(self._repo_directory, clean=True)
-                repo = self.get_repo()
+                self.run_upgrade()
+                repo, branch = self.get_repo_and_branch()
             else:
                 raise UnknownRepositoryFormat()
 
+        if not branch.supports_tags():
+            # Some repos have the right format marker but their branches do not
+            # support tags
+            self.log.debug("Branch does not support tags, upgrading")
+            self.run_upgrade()
+            repo, branch = self.get_repo_and_branch()
+            # We could set the branch here directly, but we want to run the
+            # sanity checks in the `self.branch` property, so let's make sure
+            # we invalidate the "cache".
+            self._branch = None
+
         self.repo = repo
         self.repo.lock_read()
         self.head_revision_id  # set the property
@@ -681,7 +698,7 @@
     @property
     def tags(self) -> Optional[Dict[bytes, BzrRevisionId]]:
         assert self.repo is not None
-        if self._tags is None and self.branch.supports_tags():
+        if self._tags is None:
             self._tags = {
                 n.encode(): r for n, r in self.branch.tags.get_tag_dict().items()
             }
diff --git a/swh/loader/bzr/tests/data/does-not-support-tags.sh b/swh/loader/bzr/tests/data/does-not-support-tags.sh
new file mode 100644
--- /dev/null
+++ b/swh/loader/bzr/tests/data/does-not-support-tags.sh
@@ -0,0 +1,9 @@
+#!/usr/bin/env bash
+# Creates a repository with the correct recent format but an old branch
+# format that does not support tags
+
+set -euo pipefail
+bzr init-shared-repo does-not-support-tags-repo
+cd does-not-support-tags-repo
+bzr init --knit does-not-support-tags-branch
+cd ..
\ No newline at end of file
diff --git a/swh/loader/bzr/tests/data/does-not-support-tags.tgz b/swh/loader/bzr/tests/data/does-not-support-tags.tgz
new file mode 100644
index 0000000000000000000000000000000000000000..0000000000000000000000000000000000000000
GIT binary patch
literal 0
Hc$@<O00001

literal 0
Hc$@<O00001

diff --git a/swh/loader/bzr/tests/test_loader.py b/swh/loader/bzr/tests/test_loader.py
--- a/swh/loader/bzr/tests/test_loader.py
+++ b/swh/loader/bzr/tests/test_loader.py
@@ -39,6 +39,8 @@
 #   - Ghost revisions
 # - broken-tags
 #   - Tags corruption
+# - does-not-support-tags
+#   - Repo is recent but branch does not support tags, needs upgraded
 
 # TODO tests:
 # - Root path listed in changes (does that even happen?)
@@ -139,10 +141,27 @@
     archive_path = Path(datadir, "needs-upgrade.tgz")
     repo_url = prepare_repository_from_archive(archive_path, "needs-upgrade", tmp_path)
 
-    res = BazaarLoader(swh_storage, repo_url, directory=repo_url).load()
+    loader = BazaarLoader(swh_storage, repo_url, directory=repo_url)
+    upgrade_spy = mocker.spy(loader, "run_upgrade")
+    res = loader.load()
+    upgrade_spy.assert_called()
     assert res == {"status": "uneventful"}  # needs-upgrade is an empty repo
 
 
+def test_does_not_support_tags(swh_storage, datadir, tmp_path, mocker):
+    """Repository format is correct, but the branch itself does not support tags
+    and should be upgraded to the latest format"""
+    archive_path = Path(datadir, "does-not-support-tags.tgz")
+    path = "does-not-support-tags-repo/does-not-support-tags-branch"
+    repo_url = prepare_repository_from_archive(archive_path, path, tmp_path,)
+
+    loader = BazaarLoader(swh_storage, repo_url, directory=repo_url)
+    upgrade_spy = mocker.spy(loader, "run_upgrade")
+    res = loader.load()
+    upgrade_spy.assert_called()
+    assert res == {"status": "uneventful"}  # does-not-support-tags is an empty repo
+
+
 def test_no_branch(swh_storage, datadir, tmp_path):
     """This should only happen with a broken clone, so the expected result is failure"""
     archive_path = Path(datadir, "no-branch.tgz")