diff --git a/packages/block-editor/src/components/block-inspector/index.js b/packages/block-editor/src/components/block-inspector/index.js
index 1fa6c3ea507d9..6da035a883ffb 100644
--- a/packages/block-editor/src/components/block-inspector/index.js
+++ b/packages/block-editor/src/components/block-inspector/index.js
@@ -95,7 +95,8 @@ const BlockInspector = ( { showNoBlockSelectedMessage = true } ) => {
 			blockType: _blockType,
 			topLevelLockedBlock:
 				getContentLockingParent( _selectedBlockClientId ) ||
-				( getTemplateLock( _selectedBlockClientId ) === 'contentOnly'
+				( getTemplateLock( _selectedBlockClientId ) === 'contentOnly' ||
+				_selectedBlockName === 'core/block'
 					? _selectedBlockClientId
 					: undefined ),
 		};
diff --git a/packages/block-library/src/block/edit.js b/packages/block-library/src/block/edit.js
index a274843ff37ed..79be6ffd44e85 100644
--- a/packages/block-library/src/block/edit.js
+++ b/packages/block-library/src/block/edit.js
@@ -402,7 +402,7 @@ function ReusableBlockEdit( {
 	} );
 
 	const innerBlocksProps = useInnerBlocksProps( blockProps, {
-		templateLock: 'contentOnly',
+		templateLock: 'all',
 		layout,
 		renderAppender: innerBlocks?.length
 			? undefined