diff --git a/docs/user_guide/writing_documentation.rst b/docs/user_guide/writing_documentation.rst
index 1017dc4d..721b6b19 100644
--- a/docs/user_guide/writing_documentation.rst
+++ b/docs/user_guide/writing_documentation.rst
@@ -246,6 +246,22 @@ There are three predefined macros:
 You can defined additional custom aliases with the `alias
 <option-alias>` option.
 
+.. note::
+   Because the `markdown syntax for tables
+   <https://python-markdown.github.io/extensions/tables/>`_ also uses
+   pipes, you should ensure there is whitespace around the pipes for
+   tables and **no** whitespace in aliases:
+
+   .. code:: markdown
+
+       | Table Col 1 | Table Col 2 |
+       | ----------- | ----------- |
+       | note spaces | around pipes |
+       | [link](|page|/subpage2.html) | |note_no_space_in_alias| |
+
+   This avoids clashes between the syntax for the two features.
+
+
 .. _writing-links:
 
 Links
diff --git a/ford/_markdown.py b/ford/_markdown.py
index 0286ca6a..acc25345 100644
--- a/ford/_markdown.py
+++ b/ford/_markdown.py
@@ -3,6 +3,7 @@
 from markdown import Markdown, Extension
 from markdown.inlinepatterns import InlineProcessor
 from markdown.treeprocessors import Treeprocessor
+from markdown.preprocessors import Preprocessor
 from typing import Dict, List, Union, Optional, TYPE_CHECKING
 import re
 from xml.etree.ElementTree import Element
@@ -119,24 +120,28 @@ def convert(
         return super().convert(source)
 
 
-ALIAS_RE = r"\|(.+?)\|"
-
-
-class AliasProcessor(InlineProcessor):
+class AliasPreprocessor(Preprocessor):
     """Substitute text aliases of the form ``|foo|`` from a dictionary
     of aliases and their replacements"""
 
-    def __init__(self, pattern: str, md: Markdown, aliases: Dict[str, str]):
+    ALIAS_RE = re.compile(r"\|([^ ].*?[^ ]?)\|")
+
+    def __init__(self, md: Markdown, aliases: Dict[str, str]):
         self.aliases = aliases
-        super().__init__(pattern, md)
 
-    def handleMatch(self, m: re.Match, data: str):  # type: ignore[override]
-        try:
-            sub = self.aliases[m.group(1)]
-        except KeyError:
-            return None, None, None
+        super().__init__(md)
 
-        return sub, m.start(0), m.end(0)
+    def _lookup(self, m: re.Match):
+        """Return alias replacement for match. If not found, return
+        the original text, including pipes
+
+        """
+        return self.aliases.get(m.group(1), f"|{m.group(1)}|")
+
+    def run(self, lines: List[str]) -> List[str]:
+        for line_num, line in enumerate(lines):
+            lines[line_num] = self.ALIAS_RE.sub(self._lookup, line)
+        return lines
 
 
 class AliasExtension(Extension):
@@ -148,8 +153,10 @@ def __init__(self, **kwargs):
 
     def extendMarkdown(self, md: Markdown):
         aliases = self.getConfig("aliases")
-        md.inlinePatterns.register(
-            AliasProcessor(ALIAS_RE, md, aliases=aliases), "ford_aliases", 175
+        # Needs to happen before tables to avoid clashes, see
+        # https://github.com/Fortran-FOSS-Programmers/ford/issues/604
+        md.preprocessors.register(
+            AliasPreprocessor(md, aliases=aliases), "ford_aliases", 50
         )
 
 
diff --git a/test/test_markdown.py b/test/test_markdown.py
index e72f5256..954773b6 100644
--- a/test/test_markdown.py
+++ b/test/test_markdown.py
@@ -1,5 +1,7 @@
 from ford._markdown import MetaMarkdown
 
+from textwrap import dedent
+
 
 def test_sub_alias():
     result = MetaMarkdown(aliases={"a": "b"}).convert("|a|")
@@ -13,6 +15,25 @@ def test_sub_alias_with_equals():
     assert result == "<p>b=c</p>"
 
 
+def test_sub_alias_in_table():
+    text = dedent(
+        """
+        |Table Col 1| Table Col 2 |
+        |-----------| ----------- |
+        |normal| entry |
+        | [link](|page|/subpage2.html) | |other| |
+        """
+    )
+
+    result = MetaMarkdown(
+        aliases={"page": "/home/page", "other": "some alias"}
+    ).convert(text)
+
+    assert "[link]" not in result
+    assert 'href="/home/page/subpage2.html"' in result
+    assert "some alias" in result
+
+
 def test_fix_relative_paths(tmp_path):
     base_path = tmp_path / "output"
     md = MetaMarkdown(relative=True, base_url=tmp_path / "output")