This isn't perfect (matching html with regular expressions is always a little dodgy!), but it might give you what you're after, or at least set you in the right direction:
perl -e 'undef $/;print join"\n",<>=~/HREF=\"(.*?)\"/sg' filename.html
Note that I'm guessing you want the target of the link: if not you'll have to modify the regex accordingly, but from what you've written that's probably not the problem.
[[Very quick explanation: links might cross lines, so the "undef $/" means that the whole file is sucked in as one blob. That blob is matched against the regex in list context, thus returning all the matches as an array. This array is printed out after being joined with spaces.]]
Best of luck,
Paul