diff --git a/package-lock.json b/package-lock.json
index 882f66bf089a9b..089fec0a2fd9e7 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -9952,7 +9952,7 @@
 				"re-resizable": "^6.0.0",
 				"react-dates": "^17.1.1",
 				"react-spring": "^8.0.20",
-				"reakit": "^1.0.0-rc.2",
+				"reakit": "^1.0.2",
 				"rememo": "^3.0.0",
 				"tinycolor2": "^1.4.1",
 				"uuid": "^7.0.2"
@@ -37034,21 +37034,21 @@
 			}
 		},
 		"reakit": {
-			"version": "1.0.0-rc.2",
-			"resolved": "https://registry.npmjs.org/reakit/-/reakit-1.0.0-rc.2.tgz",
-			"integrity": "sha512-+Snfc9Y/VMozEDXld3CJtvqgTyFCE67FXBmaDcvBuO3z2U/ZAHiAOBprF+ZN/QhsiVNMk1faj791vDBTokxS4w==",
+			"version": "1.0.2",
+			"resolved": "https://registry.npmjs.org/reakit/-/reakit-1.0.2.tgz",
+			"integrity": "sha512-l1yvXm9sjVGljsVxoPoSOWwsZWVMJZI7nWEgY+HqzPcsVH483F64oLamj21uCAbwpxfaEkQ/hS5g9RAbdfGEog==",
 			"requires": {
-				"@popperjs/core": "^2.3.3",
-				"body-scroll-lock": "^3.0.1",
-				"reakit-system": "^0.12.0",
+				"@popperjs/core": "^2.4.0",
+				"body-scroll-lock": "^3.0.2",
+				"reakit-system": "^0.12.1",
 				"reakit-utils": "^0.12.0",
 				"reakit-warning": "^0.3.0"
 			}
 		},
 		"reakit-system": {
-			"version": "0.12.0",
-			"resolved": "https://registry.npmjs.org/reakit-system/-/reakit-system-0.12.0.tgz",
-			"integrity": "sha512-lqesr7jmOEDEqKtPhEilCJNfYiLCeXOeU2lpPLBzO+CB2lsfF+A/NtrSpb3kuLu2mfIUSTTBxgaKdOBbfANmWA==",
+			"version": "0.12.1",
+			"resolved": "https://registry.npmjs.org/reakit-system/-/reakit-system-0.12.1.tgz",
+			"integrity": "sha512-92NRBxCHslIkME4y2Z5jPAOESiBbkOF2g0LE2FiPSzZwdJ9/geWfhP50y/WFAO1WIFChVREATSXqng1xhWGwwg==",
 			"requires": {
 				"reakit-utils": "^0.12.0"
 			}
diff --git a/packages/components/package.json b/packages/components/package.json
index 24057ff94d8a19..629ece0260c0c3 100644
--- a/packages/components/package.json
+++ b/packages/components/package.json
@@ -53,7 +53,7 @@
 		"re-resizable": "^6.0.0",
 		"react-dates": "^17.1.1",
 		"react-spring": "^8.0.20",
-		"reakit": "^1.0.0-rc.2",
+		"reakit": "^1.0.2",
 		"rememo": "^3.0.0",
 		"tinycolor2": "^1.4.1",
 		"uuid": "^7.0.2"
diff --git a/packages/components/src/alignment-matrix-control/index.js b/packages/components/src/alignment-matrix-control/index.js
index 20467dd5068e4b..a7ced8b7d451b9 100644
--- a/packages/components/src/alignment-matrix-control/index.js
+++ b/packages/components/src/alignment-matrix-control/index.js
@@ -99,10 +99,6 @@ export default function AlignmentMatrixControl( {
 								key={ cell }
 								value={ cell }
 								onFocus={ () => handleOnChange( cell ) }
-								onClick={ () =>
-									// VoiceOver doesn't focus elements on click
-									composite.move( cellId )
-								}
 							/>
 						);
 					} ) }
diff --git a/packages/components/src/alignment-matrix-control/test/index.js b/packages/components/src/alignment-matrix-control/test/index.js
index 7758d77d317ae1..eaa28941048c14 100644
--- a/packages/components/src/alignment-matrix-control/test/index.js
+++ b/packages/components/src/alignment-matrix-control/test/index.js
@@ -2,7 +2,7 @@
  * External dependencies
  */
 import { render, unmountComponentAtNode } from 'react-dom';
-import { act, Simulate } from 'react-dom/test-utils';
+import { act } from 'react-dom/test-utils';
 
 /**
  * Internal dependencies
@@ -69,15 +69,21 @@ describe( 'AlignmentMatrixControl', () => {
 
 			const cells = getCells();
 
-			act( () => Simulate.click( cells[ 3 ] ) );
+			act( () => {
+				cells[ 3 ].focus();
+			} );
 
 			expect( spy.mock.calls[ 0 ][ 0 ] ).toBe( 'center left' );
 
-			act( () => Simulate.click( cells[ 4 ] ) );
+			act( () => {
+				cells[ 4 ].focus();
+			} );
 
 			expect( spy.mock.calls[ 1 ][ 0 ] ).toBe( 'center center' );
 
-			act( () => Simulate.click( cells[ 7 ] ) );
+			act( () => {
+				cells[ 7 ].focus();
+			} );
 
 			expect( spy.mock.calls[ 2 ][ 0 ] ).toBe( 'bottom center' );
 		} );
diff --git a/packages/components/src/toolbar-item/index.js b/packages/components/src/toolbar-item/index.js
index a475eb5e8e3c79..dcfdca4ea46bc9 100644
--- a/packages/components/src/toolbar-item/index.js
+++ b/packages/components/src/toolbar-item/index.js
@@ -32,11 +32,7 @@ function ToolbarItem( { children, ...props }, ref ) {
 
 	return (
 		<BaseToolbarItem { ...accessibleToolbarState } { ...allProps }>
-			{ ( htmlProps ) =>
-				// Overwriting BaseToolbarItem's onMouseDown since it disables drag
-				// and drop
-				children( { ...htmlProps, onMouseDown: allProps.onMouseDown } )
-			}
+			{ children }
 		</BaseToolbarItem>
 	);
 }