diff --git a/packages/eui/changelogs/upcoming/8135.md b/packages/eui/changelogs/upcoming/8135.md
new file mode 100644
index 00000000000..03d2cdf4ac9
--- /dev/null
+++ b/packages/eui/changelogs/upcoming/8135.md
@@ -0,0 +1,4 @@
+**Bug fixes**
+
+-  Fixed an `EuiDataGrid` bug where column actions where not clickable when `EuiDataGrid` with `columnVisibility.canDragAndDropColumns` was used inside a modal
+
diff --git a/packages/eui/src-docs/src/views/datagrid/schema_columns/column_dragging.js b/packages/eui/src-docs/src/views/datagrid/schema_columns/column_dragging.js
index b363d54b33c..fd3e11e4d60 100644
--- a/packages/eui/src-docs/src/views/datagrid/schema_columns/column_dragging.js
+++ b/packages/eui/src-docs/src/views/datagrid/schema_columns/column_dragging.js
@@ -1,41 +1,20 @@
-import React, { useState } from 'react';
+import React, { useState, useCallback } from 'react';
 import { faker } from '@faker-js/faker';
 
-import {
-  EuiDataGrid,
-  EuiAvatar,
-  EuiToolTip,
-  EuiButtonIcon,
-} from '../../../../../src/components';
-
-const CustomHeaderCell = ({ title }) => (
-  <>
-    <span>{title}</span>
-    <EuiToolTip content="tooltip content">
-      <EuiButtonIcon
-        iconType="questionInCircle"
-        aria-label="Additional information"
-        color="primary"
-      />
-    </EuiToolTip>
-  </>
-);
+import { EuiDataGrid, EuiAvatar } from '../../../../../src/components';
 
 const columns = [
   {
     id: 'avatar',
     initialWidth: 40,
     isResizable: false,
-    actions: false,
   },
   {
     id: 'name',
-    displayAsText: 'Name',
-    display: <CustomHeaderCell title="Name" />,
+    initialWidth: 100,
   },
   {
     id: 'email',
-    display: <CustomHeaderCell title="Email" />,
   },
   {
     id: 'city',
@@ -67,21 +46,42 @@ for (let i = 1; i < 5; i++) {
 }
 
 export default () => {
+  const [pagination, setPagination] = useState({ pageIndex: 0 });
+
   const [visibleColumns, setVisibleColumns] = useState(
     columns.map(({ id }) => id)
   );
 
+  const setPageIndex = useCallback(
+    (pageIndex) =>
+      setPagination((pagination) => ({ ...pagination, pageIndex })),
+    []
+  );
+  const setPageSize = useCallback(
+    (pageSize) =>
+      setPagination((pagination) => ({
+        ...pagination,
+        pageSize,
+        pageIndex: 0,
+      })),
+    []
+  );
+
   return (
     <EuiDataGrid
-      aria-label="DataGrid demonstrating column reordering on drag"
+      aria-label="DataGrid demonstrating column sizing constraints"
       columns={columns}
       columnVisibility={{
         visibleColumns: visibleColumns,
         setVisibleColumns: setVisibleColumns,
-        canDragAndDropColumns: true,
       }}
       rowCount={data.length}
       renderCellValue={({ rowIndex, columnId }) => data[rowIndex][columnId]}
+      pagination={{
+        ...pagination,
+        onChangeItemsPerPage: setPageSize,
+        onChangePage: setPageIndex,
+      }}
     />
   );
 };
diff --git a/packages/eui/src/components/datagrid/body/header/draggable_columns.spec.tsx b/packages/eui/src/components/datagrid/body/header/draggable_columns.spec.tsx
index 7b78578823a..a8ad5d81e55 100644
--- a/packages/eui/src/components/datagrid/body/header/draggable_columns.spec.tsx
+++ b/packages/eui/src/components/datagrid/body/header/draggable_columns.spec.tsx
@@ -12,6 +12,7 @@
 
 import React, { useState } from 'react';
 import { EuiDataGrid, EuiDataGridProps } from '../../index';
+import { EuiModal, EuiModalBody } from '../../../modal';
 
 describe('draggable columns', () => {
   const columns = [
@@ -284,4 +285,40 @@ describe('draggable columns', () => {
       cy.get('[data-popover-open]').should('not.exist');
     });
   });
+
+  describe('inside a modal', () => {
+    it('should execute column actions on click', () => {
+      cy.realMount(
+        <EuiModal onClose={() => {}}>
+          <EuiModalBody>
+            <StatefulDataGrid />
+          </EuiModalBody>
+        </EuiModal>
+      );
+
+      cy.get('[data-test-subj=dataGridHeaderCell-a]').realHover();
+      cy.wait(50); // wait until actions button transition is progressed enough for the button to be clickable
+      cy.get('[data-test-subj=dataGridHeaderCellActionButton-a]').realClick();
+      cy.get('[data-popover-open]').should('have.focus');
+
+      cy.get(
+        '.euiListGroupItem:last-child .euiListGroupItem__button'
+      ).realClick();
+
+      cy.get('[data-test-subj=dataGridHeaderCell-a]').should(
+        'have.attr',
+        'data-gridcell-column-index',
+        '1'
+      );
+      cy.get('[data-test-subj=dataGridHeaderCell-b]').should(
+        'have.attr',
+        'data-gridcell-column-index',
+        '0'
+      );
+
+      cy.get('[data-test-subj=euiDataGridHeaderColumnActions]').should(
+        'not.exist'
+      );
+    });
+  });
 });
diff --git a/packages/eui/src/components/datagrid/body/header/draggable_columns.tsx b/packages/eui/src/components/datagrid/body/header/draggable_columns.tsx
index 7c754013184..be12c9a2669 100644
--- a/packages/eui/src/components/datagrid/body/header/draggable_columns.tsx
+++ b/packages/eui/src/components/datagrid/body/header/draggable_columns.tsx
@@ -132,16 +132,23 @@ export const DraggableColumn: FunctionComponent<{
     const { setFocusedCell } = useContext(DataGridFocusContext);
     const handleOnMouseDown: MouseEventHandler = useCallback(
       (e) => {
-        const openFocusTrap = document.querySelector(
+        const openFocusTraps = document.querySelectorAll(
           '[data-focus-lock-disabled="false"]'
         );
-        if (
-          !!openFocusTrap && // If a focus trap is open somewhere on the page
-          !openFocusTrap.contains(e.target as Node) && // & the focus trap doesn't belong to this header
-          e.target !== actionsPopoverToggle // & we're not closing the actions popover toggle
-        ) {
+        const validOpenFocusTraps = [...openFocusTraps].filter(
+          (focusTrap) => !focusTrap.contains(e.currentTarget as Node) // remove containing focus traps (e.g. modals or flyouts)
+        );
+
+        const shouldDispatchEvent = validOpenFocusTraps.some(
+          (focusTrap) =>
+            !!focusTrap && // If there is a focus trap open
+            !focusTrap.contains(e.target as Node) && // & if it doesn't contain the target
+            e.target !== actionsPopoverToggle // & we're not closing the actions popover toggle
+        );
+
+        if (shouldDispatchEvent) {
           // Trick the focus trap lib into registering an outside click -
-          // the drag/drop lib otherwise otherwise prevents the event 💀
+          // the drag/drop lib otherwise prevents the event 💀
           document.dispatchEvent(new MouseEvent('mousedown'));
         }
         setTimeout(() => {