Don't allow to start dragging blocks if a locking lock all exists

components/draggable/README.md

@@ -6,6 +6,14 @@
 
 The component accepts the following props:
 
+### draggable
+
+If the component is in a draggable state or not. If false, the component is rendered but it is not possible to drag it. Defaults to true.
+
+- Type: `boolean`
+- Required: No
+- Default:  `true`
+
 ### elementId
 
 The HTML id of the element to clone on drag

components/draggable/index.js

@@ -152,13 +152,13 @@ class Draggable extends Component {
 	}
 
 	render() {
-		const { children, className } = this.props;
+		const { children, draggable = true, className } = this.props;
 		return (
 			<div
 				className={ classnames( 'components-draggable', className ) }
 				onDragStart={ this.onDragStart }
 				onDragEnd={ this.onDragEnd }
-				draggable
+				draggable={ draggable }
 			>
 				{ children }
 			</div>

editor/components/block-list/block.js

@@ -414,6 +414,7 @@ export class BlockListBlock extends Component {
 			isEmptyDefaultBlock,
 			isPreviousBlockADefaultEmptyBlock,
 			hasSelectedInnerBlock,
+			templateLock,
 		} = this.props;
 		const isHovered = this.state.isHovered && ! isMultiSelecting;
 		const { name: blockName, isValid } = block;
@@ -504,6 +505,7 @@ export class BlockListBlock extends Component {
 						onDragEnd={ this.onDragEnd }
 						isDragging={ dragging }
 						elementId={ blockElementId }
+						draggable={ 'all' !== templateLock } // only in locking all moving blocks is totally impossible
 					/>
 				) }
 				{ shouldShowInsertionPoint && (
@@ -646,6 +648,7 @@ const applyWithSelect = withSelect( ( select, { uid, rootUID } ) => {
 		initialPosition: getSelectedBlocksInitialCaretPosition(),
 		isEmptyDefaultBlock: block && isUnmodifiedDefaultBlock( block ),
 		isPreviousBlockADefaultEmptyBlock: previousBlock && isUnmodifiedDefaultBlock( previousBlock ),
+		templateLock,
 		isLocked: !! templateLock,
 		previousBlockUid,
 		block,

editor/components/block-list/style.scss

@@ -74,9 +74,10 @@
 		}
 	}
 
-
-	cursor: move; // Fallback for IE/Edge < 14
-	cursor: grab;
+	&[draggable=true]{
+		cursor: move; // Fallback for IE/Edge < 14
+		cursor: grab;
+	}
 }