Use the answer by @Alec if you're only looking for the base url part (the 2nd part of the question by @David)!
$html = '<a href="http://www.mydomain.com/page.html" class="myclass" rel="myrel">URL</a>';
$url = preg_match('/<a href="(.+)">/', $html, $match);
$info = parse_url($match[1]);
This will give you:
$info
Array
(
[scheme] => http
[host] => www.mydomain.com
[path] => /page.html" class="myclass" rel="myrel
)
So you can use $href = $info["scheme"] . "://" . $info["host"]
Which gives you:
// http://www.mydomain.com
When you are looking for the entire url between the href, You should be using another regex, for instance the regex provided by @user2520237.
$html = '<a href="http://www.mydomain.com/page.html" class="myclass" rel="myrel">URL</a>';
$url = preg_match('/href=["\']?([^"\'>]+)["\']?/', $html, $match);
$info = parse_url($match[1]);
this will give you:
$info
Array
(
[scheme] => http
[host] => www.mydomain.com
[path] => /page.html
)
Now you can use $href = $info["scheme"] . "://" . $info["host"] . $info["path"];
Which gives you:
// http://www.mydomain.com/page.html