wp_remote_get Response could not be parsed

Yeah, something their host needs to resolve. To avoid a common knee jerk response like “It’s not us, it’s a WP problem”, it would be telling to see the actual headers, if any, of a typical response. They could put the following into a new PHP file and request the file, then report the result.

<?php
if ( ! in_array('curl', get_loaded_extensions())) die('cURL not available');

$url = 'https://canalplan.org.uk/cgi-bin/api.cgi?mode=version';
$ch = curl_init();
  curl_setopt($ch, CURLOPT_URL, $url);
  curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
  curl_setopt($ch, CURLOPT_HEADER, 1);

  $response = curl_exec($ch);
  
  $header_size = curl_getinfo($ch, CURLINFO_HEADER_SIZE);
  $headers = substr($response, 0, $header_size);
curl_close($ch);

header("Content-Type:text/plain; charset=UTF-8");
echo "Header size: $header_size<br>\n";
echo $headers;

You probably noticed by now, but the <br> tag in the second to last line should be removed since the content type is not HTML.

It’s not my call, but I would say no to putting it in health-check at this time. Health-check did its job by flagging the error. Actually seeing the headers returned can be determined any number of ways. This is probably a very rare server or network device misconfiguration. If it turns out to be a more common issue, then I could see including something. I’m leery of contributing to feature bloat for a one-off situation.

Regardless of what I think, you can add a feature request or even contribute to the project on github.