Don't use regexes. Use an HTML parser like HTML::TreeBuilder.
my @links;
my $tree = HTML::TreeBuilder->new; # empty tree
$tree->parse_file($file_name);
$tree->elementify;
my @links = map { $_->attr('href') } $tree->look_down( _tag => 'a');
$tree = $tree->delete;
# Do stuff with links array