diff --git a/packages/block-library/src/column/edit.js b/packages/block-library/src/column/edit.js
index 1664bff4ffeb59..e815731970d320 100644
--- a/packages/block-library/src/column/edit.js
+++ b/packages/block-library/src/column/edit.js
@@ -23,6 +23,7 @@ function ColumnEdit( {
 	setAttributes,
 	updateAlignment,
 	hasChildBlocks,
+	columnsParentLock,
 } ) {
 	const { verticalAlignment, width } = attributes;
 
@@ -60,7 +61,11 @@ function ColumnEdit( {
 				</PanelBody>
 			</InspectorControls>
 			<InnerBlocks
-				templateLock={ false }
+				// It is safe to set an "inherited" locking explicitly because no
+				// template is set on the column. If a template was set and parent lock
+				// was equal to "all" the local template set would be forced and other
+				// templates passed e.g via CPT would be ignored.
+				templateLock={ columnsParentLock }
 				renderAppender={
 					hasChildBlocks
 						? undefined
@@ -79,10 +84,20 @@ function ColumnEdit( {
 export default compose(
 	withSelect( ( select, ownProps ) => {
 		const { clientId } = ownProps;
-		const { getBlockOrder } = select( 'core/block-editor' );
+		const { getBlockOrder, getBlockRootClientId, getTemplateLock } = select(
+			'core/block-editor'
+		);
+
+		const parentColumnsId = getBlockRootClientId( clientId );
+		const parentOfColumnsId = getBlockRootClientId( parentColumnsId );
+		const columnsParentLock = parentOfColumnsId
+			? getTemplateLock( parentOfColumnsId )
+			: getTemplateLock();
 
 		return {
 			hasChildBlocks: getBlockOrder( clientId ).length > 0,
+			columnsParentLock:
+				columnsParentLock !== undefined ? columnsParentLock : false,
 		};
 	} ),
 	withDispatch( ( dispatch, ownProps, registry ) => {