diff --git a/packages/govuk-frontend/src/govuk/components/skip-link/skip-link.mjs b/packages/govuk-frontend/src/govuk/components/skip-link/skip-link.mjs
index d477a25b4a..8d4db24fc4 100644
--- a/packages/govuk-frontend/src/govuk/components/skip-link/skip-link.mjs
+++ b/packages/govuk-frontend/src/govuk/components/skip-link/skip-link.mjs
@@ -21,6 +21,7 @@ export class SkipLink extends GOVUKFrontendComponent {
 
   /**
    * @param {Element} $module - HTML element to use for skip link
+   * @throws {MissingElementError} If the element with the specified ID is not found
    */
   constructor($module) {
     super()
@@ -35,12 +36,9 @@ export class SkipLink extends GOVUKFrontendComponent {
     try {
       const $linkedElement = this.getLinkedElement()
       this.$linkedElement = $linkedElement
-    } catch (cause) {
+    } catch (err) {
       throw new MissingElementError(
-        'Skip link: the linked HTML element does not exist',
-        {
-          cause: cause instanceof Error ? cause : undefined
-        }
+        `Skip link: ${err instanceof Error ? err.message : ''}`
       )
     }
 
@@ -52,23 +50,19 @@ export class SkipLink extends GOVUKFrontendComponent {
    *
    * @private
    * @throws {Error} If the "href" attribute does not contain a hash
-   * @throws {Error} If the element with the specified ID does not exist
+   * @throws {TypeError} If the element with the specified ID is not found
    * @returns {HTMLElement} $linkedElement - DOM element linked to from the skip link
    */
   getLinkedElement() {
     const linkedElementId = this.getFragmentFromUrl()
     if (!linkedElementId) {
-      throw new Error(
-        `Skip link: $module "href" attribute does not contain a hash`
-      )
+      throw new Error(`$module "href" attribute does not contain a hash`)
     }
 
     const linkedElement = document.getElementById(linkedElementId)
 
     if (!linkedElement) {
-      throw new Error(
-        `Skip link: Target selector "#${linkedElementId}" not found`
-      )
+      throw new TypeError(`Target selector "#${linkedElementId}" not found`)
     }
 
     return linkedElement
diff --git a/packages/govuk-frontend/src/govuk/components/skip-link/skip-link.test.js b/packages/govuk-frontend/src/govuk/components/skip-link/skip-link.test.js
index b3e3cf1e56..9e0cef51dc 100644
--- a/packages/govuk-frontend/src/govuk/components/skip-link/skip-link.test.js
+++ b/packages/govuk-frontend/src/govuk/components/skip-link/skip-link.test.js
@@ -92,7 +92,22 @@ describe('Skip Link', () => {
         })
       ).rejects.toEqual({
         name: 'MissingElementError',
-        message: 'Skip link: the linked HTML element does not exist'
+        message:
+          'Skip link: Target selector "#this-element-does-not-exist" not found'
+      })
+    })
+
+    it('throws when the href does not contain a hash', async () => {
+      await expect(
+        renderAndInitialise(page, 'skip-link', {
+          params: {
+            text: 'Skip to main content',
+            href: 'this-element-does-not-exist'
+          }
+        })
+      ).rejects.toEqual({
+        name: 'MissingElementError',
+        message: 'Skip link: $module "href" attribute does not contain a hash'
       })
     })
   })