diff --git a/core/modules/block/src/Tests/BlockUiTest.php b/core/modules/block/src/Tests/BlockUiTest.php
index 25b7942..cf17938 100644
--- a/core/modules/block/src/Tests/BlockUiTest.php
+++ b/core/modules/block/src/Tests/BlockUiTest.php
@@ -83,13 +83,16 @@ protected function setUp() {
   public function testBlockDemoUiPage() {
     $this->drupalPlaceBlock('help_block', array('region' => 'help'));
     $this->drupalGet('admin/structure/block');
-    $this->clickLink(t('Demonstrate block regions (@theme)', array('@theme' => 'Classy')));
+    $this->clickLink(t('Demonstrate block regions (@theme)', array('@theme' => 'Test Classy')));
     $elements = $this->xpath('//div[contains(@class, "region-highlighted")]/div[contains(@class, "block-region") and contains(text(), :title)]', array(':title' => 'Highlighted'));
     $this->assertTrue(!empty($elements), 'Block demo regions are shown.');
 
     \Drupal::service('theme_handler')->install(array('test_theme'));
     $this->drupalGet('admin/structure/block/demo/test_theme');
     $this->assertEscaped('<strong>Test theme</strong>');
+
+    $this->drupalGet('admin/structure/block/demo/classy');
+    $this->assertResponse(403, 'Hidden themes cannot are not supported by the block demo screen');
   }
 
   /**
@@ -136,6 +139,20 @@ function testBlockAdminUiPage() {
     $this->drupalGet('admin/structure/block');
     $element = $this->xpath('//tr[contains(@class, :class)]', [':class' => 'region-title-header']);
     $this->assertTrue(!empty($element));
+
+    // Ensure hidden themes do not appear in the UI. Enable another non base
+    // theme and place the local tasks block.
+    $this->assertTrue(\Drupal::service('theme_handler')->themeExists('classy'), 'The classy base theme is enabled');
+    $this->drupalPlaceBlock('local_tasks_block', ['region' => 'header']);
+    \Drupal::service('theme_installer')->install(['test_theme']);
+    $this->drupalGet('admin/structure/block');
+    $theme_handler = \Drupal::service('theme_handler');
+    $this->assertLink($theme_handler->getName('test_classy'));
+    $this->assertLink($theme_handler->getName('test_theme'));
+    $this->assertNoLink($theme_handler->getName('classy'));
+
+    $this->drupalGet('admin/structure/block/list/classy');
+    $this->assertResponse(403, 'Placing blocks through UI is not possible for the base theme classy.');
   }
 
   /**
@@ -145,7 +162,7 @@ public function testCandidateBlockList() {
     $arguments = array(
       ':title' => 'Display message',
       ':category' => 'Block test',
-      ':href' => 'admin/structure/block/add/test_block_instantiation/classy',
+      ':href' => 'admin/structure/block/add/test_block_instantiation/test_classy',
     );
     $pattern = '//tr[.//td/div[text()=:title] and .//td[text()=:category] and .//td//a[contains(@href, :href)]]';
 
@@ -171,7 +188,7 @@ public function testCandidateBlockList() {
   public function testContextAwareUnsatisfiedBlocks() {
     $arguments = array(
       ':category' => 'Block test',
-      ':href' => 'admin/structure/block/add/test_context_aware_unsatisfied/classy',
+      ':href' => 'admin/structure/block/add/test_context_aware_unsatisfied/test_classy',
       ':text' => 'Test context-aware unsatisfied block',
     );
 
@@ -193,7 +210,7 @@ public function testContextAwareBlocks() {
     $this->assertNoText('Test context-aware block');
     $this->assertNoRaw($expected_text);
 
-    $block_url = 'admin/structure/block/add/test_context_aware/classy';
+    $block_url = 'admin/structure/block/add/test_context_aware/test_classy';
     $arguments = array(
       ':title' => 'Test context-aware block',
       ':category' => 'Block test',
@@ -231,7 +248,7 @@ public function testContextAwareBlocks() {
    * Tests that the BlockForm populates machine name correctly.
    */
   public function testMachineNameSuggestion() {
-    $url = 'admin/structure/block/add/test_block_instantiation/classy';
+    $url = 'admin/structure/block/add/test_block_instantiation/test_classy';
     $this->drupalGet($url);
     $this->assertFieldByName('id', 'displaymessage', 'Block form uses raw machine name suggestion when no instance already exists.');
     $this->drupalPostForm($url, array(), 'Save block');
@@ -253,16 +270,16 @@ public function testBlockPlacementIndicator() {
     // Select the 'Powered by Drupal' block to be placed.
     $block = array();
     $block['id'] = strtolower($this->randomMachineName());
-    $block['theme'] = 'classy';
+    $block['theme'] = 'test_classy';
     $block['region'] = 'content';
 
     // After adding a block, it will indicate which block was just added.
     $this->drupalPostForm('admin/structure/block/add/system_powered_by_block', $block, t('Save block'));
-    $this->assertUrl('admin/structure/block/list/classy?block-placement=' . Html::getClass($block['id']));
+    $this->assertUrl('admin/structure/block/list/test_classy?block-placement=' . Html::getClass($block['id']));
 
     // Resaving the block page will remove the block indicator.
     $this->drupalPostForm(NULL, array(), t('Save blocks'));
-    $this->assertUrl('admin/structure/block/list/classy');
+    $this->assertUrl('admin/structure/block/list/test_classy');
   }
 
 }
diff --git a/core/modules/block/tests/modules/block_test/config/install/block.block.test_block.yml b/core/modules/block/tests/modules/block_test/config/install/block.block.test_block.yml
index be7e06c..32f8e95 100644
--- a/core/modules/block/tests/modules/block_test/config/install/block.block.test_block.yml
+++ b/core/modules/block/tests/modules/block_test/config/install/block.block.test_block.yml
@@ -13,5 +13,5 @@ dependencies:
   module:
     - block_test
   theme:
-    - classy
+    - test_classy
 visibility: {  }
diff --git a/core/modules/block_content/src/Tests/BlockContentTypeTest.php b/core/modules/block_content/src/Tests/BlockContentTypeTest.php
index e669a72..e176e56 100644
--- a/core/modules/block_content/src/Tests/BlockContentTypeTest.php
+++ b/core/modules/block_content/src/Tests/BlockContentTypeTest.php
@@ -186,16 +186,14 @@ public function testsBlockContentAddTypes() {
 
     // Install all themes.
     \Drupal::service('theme_handler')->install(array('bartik', 'seven'));
-    $themes = array('bartik', 'seven', 'classy');
     $theme_settings = $this->config('system.theme');
-    foreach ($themes as $default_theme) {
+    foreach (['bartik', 'seven', 'test_classy'] as $default_theme) {
       // Change the default theme.
       $theme_settings->set('default', $default_theme)->save();
       \Drupal::service('router.builder')->rebuild();
 
       // For each installed theme, go to its block page and test the redirects.
-      $themes = array('bartik', 'classy', 'seven');
-      foreach ($themes as $theme) {
+      foreach (['bartik', 'test_classy', 'seven'] as $theme) {
         // Test that adding a block from the 'place blocks' form sends you to the
         // block configure form.
         $path = $theme == $default_theme ? 'admin/structure/block' : "admin/structure/block/list/$theme";
diff --git a/core/modules/block_content/tests/modules/block_content_test/config/install/block.block.foobargorilla.yml b/core/modules/block_content/tests/modules/block_content_test/config/install/block.block.foobargorilla.yml
index 42858f7..49fbc53 100644
--- a/core/modules/block_content/tests/modules/block_content_test/config/install/block.block.foobargorilla.yml
+++ b/core/modules/block_content/tests/modules/block_content_test/config/install/block.block.foobargorilla.yml
@@ -4,9 +4,9 @@ dependencies:
   module:
     - block_content
   theme:
-    - classy
+    - test_classy
 id: foobargorilla
-theme: classy
+theme: test_classy
 region: content
 weight: null
 provider: null