diff --git a/docs/src/conf.py b/docs/src/conf.py
index b5cdb67f3a..3636f94d1b 100644
--- a/docs/src/conf.py
+++ b/docs/src/conf.py
@@ -358,8 +358,6 @@ def _dotv(version):
     "http://www.esrl.noaa.gov/psd/data/gridded/conventions/cdc_netcdf_standard.shtml",
     "http://www.nationalarchives.gov.uk/doc/open-government-licence",
     "https://www.metoffice.gov.uk/",
-    # TODO: try removing this again in future - was raising an SSLError.
-    "http://www.ecmwf.int/",
 ]
 
 # list of sources to exclude from the build.
diff --git a/docs/src/installing.rst b/docs/src/installing.rst
index 6a2d2f6131..b2481973c0 100644
--- a/docs/src/installing.rst
+++ b/docs/src/installing.rst
@@ -14,7 +14,7 @@ Subsystem for Linux).  This is a great option to get started with Iris
 for users and developers.  Be aware that we do not currently test against
 any WSL_ distributions.
 
-.. _WSL: https://docs.microsoft.com/en-us/windows/wsl/install-win10
+.. _WSL: https://learn.microsoft.com/en-us/windows/wsl/install
 
 .. note:: Iris is currently supported and tested against |python_support|
           running on Linux.  We do not currently actively test on other
diff --git a/docs/src/whatsnew/1.0.rst b/docs/src/whatsnew/1.0.rst
index b226dc609b..c256c33566 100644
--- a/docs/src/whatsnew/1.0.rst
+++ b/docs/src/whatsnew/1.0.rst
@@ -147,8 +147,7 @@ the surface pressure. In return, it provides a virtual "pressure"
 coordinate whose values are derived from the given components.
 
 This facility is utilised by the GRIB2 loader to automatically provide
-the derived "pressure" coordinate for certain data [#f1]_ from the
-`ECMWF <http://www.ecmwf.int/>`_.
+the derived "pressure" coordinate for certain data [#f1]_ from the ECMWF.
 
 .. [#f1] Where the level type is either 105 or 119, and where the
          surface pressure has an ECMWF paramId of
diff --git a/docs/src/whatsnew/latest.rst b/docs/src/whatsnew/latest.rst
index cf4b646841..06a116c5d7 100644
--- a/docs/src/whatsnew/latest.rst
+++ b/docs/src/whatsnew/latest.rst
@@ -76,6 +76,9 @@ This document explains the changes made to Iris for this release
    :obj:`~iris.analysis.MEDIAN` docstring, noting that the former handles lazy
    data. (:pull:`5128`)
 
+#. `@trexfeathers`_ updated the WSL link to Microsoft's latest documentation,
+   and removed an ECMWF link in the ``v1.0`` What's New that was failing the
+   linkcheck CI. (:pull:`5109`)
 
 💼 Internal
 ===========